Chatzidakis, Zoé; Pillay, Anand Generalized Picard-Vessiot extensions and differential Galois cohomology. (English. French summary) Zbl 1447.12003 Ann. Fac. Sci. Toulouse, Math. (6) 28, No. 5, 813-830 (2019). Reviewer: Mykola Grygorenko (Kyïv) MSC: 12H05 03C98 PDF BibTeX XML Cite \textit{Z. Chatzidakis} and \textit{A. Pillay}, Ann. Fac. Sci. Toulouse, Math. (6) 28, No. 5, 813--830 (2019; Zbl 1447.12003) Full Text: DOI arXiv OpenURL
Crespo, Teresa; Hajto, Zbigniew Picard-Vessiot extensions of real differential fields. (English) Zbl 1447.12004 SIGMA, Symmetry Integrability Geom. Methods Appl. 15, Paper 100, 11 p. (2019). Reviewer: Mykola Grygorenko (Kyïv) MSC: 12H05 13B05 14P05 12D15 PDF BibTeX XML Cite \textit{T. Crespo} and \textit{Z. Hajto}, SIGMA, Symmetry Integrability Geom. Methods Appl. 15, Paper 100, 11 p. (2019; Zbl 1447.12004) Full Text: DOI OpenURL
Pillay, Anand The Picard-Vessiot theory, constrained cohomology, and linear differential algebraic groups. (English. French summary) Zbl 1430.12009 J. Math. Pures Appl. (9) 108, No. 6, 809-817 (2017). Reviewer: Mykola Grygorenko (Kyïv) MSC: 12H05 12G05 03C45 34M15 PDF BibTeX XML Cite \textit{A. Pillay}, J. Math. Pures Appl. (9) 108, No. 6, 809--817 (2017; Zbl 1430.12009) Full Text: DOI arXiv OpenURL
Maurischat, Andreas A categorical approach to Picard-Vessiot theory. (English) Zbl 1388.13022 Theory Appl. Categ. 32, 488-525 (2017). Reviewer: Nikolay I. Kryuchkov (Ryazan) MSC: 13B05 18D10 12H20 PDF BibTeX XML Cite \textit{A. Maurischat}, Theory Appl. Categ. 32, 488--525 (2017; Zbl 1388.13022) Full Text: arXiv EMIS OpenURL
Crespo, Teresa; Hajto, Zbigniew; Sowa-Adamus, Elżbieta Galois correspondence theorem for Picard-Vessiot extensions. (English) Zbl 1331.12010 Arnold Math. J. 2, No. 1, 21-27 (2016). MSC: 12H05 12F10 PDF BibTeX XML Cite \textit{T. Crespo} et al., Arnold Math. J. 2, No. 1, 21--27 (2016; Zbl 1331.12010) Full Text: DOI arXiv OpenURL
Crespo, Teresa; Hajto, Zbigniew Real Liouville extensions. (English) Zbl 1370.12002 Commun. Algebra 43, No. 5, 2089-2093 (2015). Reviewer: Mykola Grygorenko (Kyïv) MSC: 12H05 12D15 14P05 13B05 PDF BibTeX XML Cite \textit{T. Crespo} and \textit{Z. Hajto}, Commun. Algebra 43, No. 5, 2089--2093 (2015; Zbl 1370.12002) Full Text: DOI arXiv Link OpenURL
Wibmer, Michael An intrinsic characterization of Picard-Vessiot extensions. (English) Zbl 1377.12003 J. Algebra 408, 183-188 (2014). MSC: 12H05 12F10 PDF BibTeX XML Cite \textit{M. Wibmer}, J. Algebra 408, 183--188 (2014; Zbl 1377.12003) Full Text: DOI arXiv OpenURL
Brezhnev, Yurii V. Spectral/quadrature duality: Picard-Vessiot theory and finite-gap potentials. (English) Zbl 1248.81032 Acosta-Humánez, Primitivo B. (ed.) et al., Algebraic aspects of Darboux transformations, quantum integrable systems and supersymmetric quantum mechanics, Jairo Charris Seminar 2010, Santa Maria, Colombia, August 2010. Providence, RI: American Mathematical Society (AMS); Bogota: Instituto de Matemáticas y sus Aplicaciones (IMA). (ISBN 978-0-8218-7584-1/pbk). Contemporary Mathematics 563, 1-31 (2012). MSC: 81Q05 81Q10 81U15 14K12 12H05 34L40 PDF BibTeX XML Cite \textit{Y. V. Brezhnev}, Contemp. Math. 563, 1--31 (2012; Zbl 1248.81032) Full Text: arXiv OpenURL
Duval, Guillaume Valuations and differential Galois groups. (English) Zbl 1248.12003 Mem. Am. Math. Soc. 998, vii, 68 p. (2011). Reviewer: Mykola Grygorenko (Kyïv) MSC: 12H05 12-02 34M15 12J20 PDF BibTeX XML Cite \textit{G. Duval}, Valuations and differential Galois groups. Providence, RI: American Mathematical Society (AMS) (2011; Zbl 1248.12003) Full Text: DOI OpenURL
Sowa, Elżbieta Picard-Vessiot extensions for real fields. (English) Zbl 1252.12006 Proc. Am. Math. Soc. 139, No. 7, 2407-2413 (2011). Reviewer: Sonia Rueda (Madrid) MSC: 12H05 12F10 12D15 PDF BibTeX XML Cite \textit{E. Sowa}, Proc. Am. Math. Soc. 139, No. 7, 2407--2413 (2011; Zbl 1252.12006) Full Text: DOI OpenURL
Crespo, Teresa; Hajto, Zbigniew Algebraic groups and differential Galois theory. (English) Zbl 1215.12001 Graduate Studies in Mathematics 122. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-5318-4/hbk). xiv, 225 p. (2011). Reviewer: Werner Kleinert (Berlin) MSC: 12-01 12H05 13B05 14A05 17B45 20G15 34M35 12H20 14L35 PDF BibTeX XML Cite \textit{T. Crespo} and \textit{Z. Hajto}, Algebraic groups and differential Galois theory. Providence, RI: American Mathematical Society (AMS) (2011; Zbl 1215.12001) Full Text: arXiv OpenURL
Moreno, Javier Iterative differential Galois theory in positive characteristic: a model theoretic approach. (English) Zbl 1225.03041 J. Symb. Log. 76, No. 1, 125-142 (2011). MSC: 03C60 12H05 PDF BibTeX XML Cite \textit{J. Moreno}, J. Symb. Log. 76, No. 1, 125--142 (2011; Zbl 1225.03041) Full Text: DOI arXiv OpenURL
Maurischat, Andreas Infinitesimal group schemes as iterative differential Galois groups. (English) Zbl 1193.13027 J. Pure Appl. Algebra 214, No. 11, 2092-2100 (2010). Reviewer: John N. Mordeson (Omaha) MSC: 13N99 12H05 12F15 PDF BibTeX XML Cite \textit{A. Maurischat}, J. Pure Appl. Algebra 214, No. 11, 2092--2100 (2010; Zbl 1193.13027) Full Text: DOI arXiv OpenURL
Juan, Lourdes; Magid, Andy R. Differential ‘Galois’ extensions with new constants. (English) Zbl 1206.12004 C. R., Math., Acad. Sci. Paris 348, No. 9-10, 487-490 (2010). Reviewer: Primitivo Belén Acosta-Humánez (Bogotá) MSC: 12H05 34A05 12F10 12H20 20G15 PDF BibTeX XML Cite \textit{L. Juan} and \textit{A. R. Magid}, C. R., Math., Acad. Sci. Paris 348, No. 9--10, 487--490 (2010; Zbl 1206.12004) Full Text: DOI OpenURL
Kamensky, Moshe Definable groups of partial automorphisms. (English) Zbl 1184.03028 Sel. Math., New Ser. 15, No. 2, 295-341 (2009). MSC: 03C60 03C40 12F10 12H10 12L12 PDF BibTeX XML Cite \textit{M. Kamensky}, Sel. Math., New Ser. 15, No. 2, 295--341 (2009; Zbl 1184.03028) Full Text: DOI arXiv Link OpenURL
Chinburg, Ted; Juan, Lourdes; Magid, Andy R. Picard-Vessiot extensions with specified Galois group. (English) Zbl 1220.12002 Pac. J. Math. 243, No. 2, 233-242 (2009). Reviewer: Mykola Grygorenko (Kyïv) MSC: 12H05 34M15 PDF BibTeX XML Cite \textit{T. Chinburg} et al., Pac. J. Math. 243, No. 2, 233--242 (2009; Zbl 1220.12002) Full Text: DOI OpenURL
Marinescu, B.; Bourlès, H. An intrinsic algebraic setting for poles and zeros of linear time-varying systems. (English) Zbl 1159.93015 Syst. Control Lett. 58, No. 4, 248-253 (2009). MSC: 93B55 93C05 93D09 PDF BibTeX XML Cite \textit{B. Marinescu} and \textit{H. Bourlès}, Syst. Control Lett. 58, No. 4, 248--253 (2009; Zbl 1159.93015) Full Text: DOI OpenURL
Acosta Humánez, Primitivo B.; Pérez Alcázar, Jesús Hernando Differential Galois theory: an approximation. (Teoría de Galois diferencial: una aproximación.) (Spanish. English summary) Zbl 1207.12004 Mat., Enseñ. Univ. (N.S.) 15, No. 2, 91-102 (2007). MSC: 12H05 34M15 PDF BibTeX XML Cite \textit{P. B. Acosta Humánez} and \textit{J. H. Pérez Alcázar}, Mat., Enseñ. Univ. (N.S.) 15, No. 2, 91--102 (2007; Zbl 1207.12004) OpenURL
Juan, Lourdes Generic Picard-Vessiot extensions for connected-by-finite groups. (English) Zbl 1183.20054 J. Algebra 312, No. 1, 194-206 (2007). MSC: 20G15 12F12 PDF BibTeX XML Cite \textit{L. Juan}, J. Algebra 312, No. 1, 194--206 (2007; Zbl 1183.20054) Full Text: DOI OpenURL
Bronstein, Manuel; Li, Ziming; Wu, Min Picard-Vessiot extensions for linear functional systems. (English) Zbl 1360.12005 Kauers, Manuel (ed.), Proceedings of the 2005 international symposium on symbolic and algebraic computation, ISSAC’05, Beijing, China, July 24–27, 2005. New York, NY: ACM Press (ISBN 1-59593-095-7). 68-75 (2005). MSC: 12H05 12H20 12Y05 35A08 68W30 PDF BibTeX XML Cite \textit{M. Bronstein} et al., in: Proceedings of the 2005 international symposium on symbolic and algebraic computation, ISSAC'05, Beijing, China, July 24--27, 2005. New York, NY: ACM Press. 68--75 (2005; Zbl 1360.12005) Full Text: DOI Link OpenURL
Amano, Katsutoshi; Masuoka, Akira Picard-Vessiot extensions of Artinian simple module algebras. (English) Zbl 1107.16037 J. Algebra 285, No. 2, 743-767 (2005). Reviewer: Hirokazu Nishimura (Tsukuba) MSC: 16T05 12H05 12H10 34M55 PDF BibTeX XML Cite \textit{K. Amano} and \textit{A. Masuoka}, J. Algebra 285, No. 2, 743--767 (2005; Zbl 1107.16037) Full Text: DOI OpenURL
Chambert-Loir, Antoine A field guide to algebra. (English) Zbl 1155.12001 Undergraduate Texts in Mathematics. New York, NY: Springer (ISBN 0-387-21428-3/hbk). x, 195 p. (2005). Reviewer: Werner Kleinert (Berlin) MSC: 12-01 12Fxx 12H20 20-01 34M15 PDF BibTeX XML Cite \textit{A. Chambert-Loir}, A field guide to algebra. New York, NY: Springer (2005; Zbl 1155.12001) OpenURL
Khovanskij, A. G. On the solvability and unsolvability of equations in explicit form. (English. Russian original) Zbl 1069.34133 Russ. Math. Surv. 59, No. 4, 661-736 (2004); translation from Usp. Mat. Nauk 59, No. 4, 69-146 (2004). Reviewer: J. Saurer (Regensburg) MSC: 34M35 34A05 12F10 12H99 34A30 34-02 PDF BibTeX XML Cite \textit{A. G. Khovanskij}, Russ. Math. Surv. 59, No. 4, 661--736 (2004; Zbl 1069.34133); translation from Usp. Mat. Nauk 59, No. 4, 69--146 (2004) Full Text: DOI OpenURL
Oberlies, Thomas Embedding problems in differential Galois theory. (Einbettungsprobleme in der Differentialgaloistheorie.) (English) Zbl 1091.12003 Heidelberg: Universität Heidelberg, Naturwissenschaftlich-Mathematische Gesamtfakultät (Dissertation). 63 p. (2003). Reviewer: E. V. Pankrat’ev (Moskva) MSC: 12H05 12F10 PDF BibTeX XML Cite \textit{T. Oberlies}, Einbettungsprobleme in der Differential\-galoistheorie. Heidelberg: Universität Heidelberg, Naturwissenschaftlich-Mathematische Gesamtfakultät (Dissertation) (2003; Zbl 1091.12003) Full Text: Link OpenURL
Bertrand, D.; Zudilin, W. On the transcendence degree of the differential field generated by Siegel modular forms. (English) Zbl 1130.11020 J. Reine Angew. Math. 554, 47-68 (2003). Reviewer: Mykola Ya. Komarnytskyy (Lviv) MSC: 11F46 12H05 PDF BibTeX XML Cite \textit{D. Bertrand} and \textit{W. Zudilin}, J. Reine Angew. Math. 554, 47--68 (2003; Zbl 1130.11020) Full Text: DOI arXiv OpenURL
Fahim, A. Galois extensions of differential algebras. (Extensions galoisiennes d’algèbres différentielles.) (French) Zbl 0903.12004 Pac. J. Math. 180, No. 1, 7-40 (1997). Reviewer: A.R.Magid (Norman) MSC: 12H05 13N99 12F20 12F10 13H99 PDF BibTeX XML Cite \textit{A. Fahim}, Pac. J. Math. 180, No. 1, 7--40 (1997; Zbl 0903.12004) Full Text: DOI OpenURL
van der Put, Marius; Singer, Michael F. Galois theory of difference equations. (English) Zbl 0930.12006 Lecture Notes in Mathematics. 1666. Berlin: Springer. vii, 180 p. (1997). Reviewer: Andy R. Magid (Norman) MSC: 12H10 12-02 39A10 PDF BibTeX XML Cite \textit{M. van der Put} and \textit{M. F. Singer}, Galois theory of difference equations. Berlin: Springer (1997; Zbl 0930.12006) Full Text: DOI OpenURL
Mitschi, C.; Singer, M. F. Connected linear groups as differential Galois groups. (English) Zbl 0867.12004 J. Algebra 184, No. 1, 333-361 (1996). Reviewer: A.R.Magid (Norman) MSC: 12H05 12F20 PDF BibTeX XML Cite \textit{C. Mitschi} and \textit{M. F. Singer}, J. Algebra 184, No. 1, 333--361 (1996; Zbl 0867.12004) Full Text: DOI Link OpenURL
Marker, D.; Messmer, M.; Pillay, A. Model theory of fields. (English) Zbl 0911.12005 Lecture Notes in Logic. 5. Berlin: Springer-Verlag. ix, 154 p. (1996). Reviewer: Salma Kuhlmann (Saskatoon) MSC: 12L12 12-02 03-02 03C60 03C10 12H05 03C45 PDF BibTeX XML Cite \textit{D. Marker} et al., Model theory of fields. Berlin: Springer-Verlag (1996; Zbl 0911.12005) OpenURL
Bhandari, A. K.; Sankaran, N. Generic differential equations and Picard-Vessiot extensions. (English) Zbl 0831.12003 Rend. Semin. Mat., Torino 52, No. 4, 353-358 (1994). Reviewer: G.Christol (Paris) MSC: 12H05 34G10 PDF BibTeX XML Cite \textit{A. K. Bhandari} and \textit{N. Sankaran}, Rend. Semin. Mat., Torino 52, No. 4, 353--358 (1994; Zbl 0831.12003) OpenURL
Magid, Andy R. Lectures on differential Galois theory. (English) Zbl 0855.12001 University Lecture Series. 7. Providence, RI: American Mathematical Society (AMS). xiii, 104 p. (1994). Reviewer: E.V.Pankrat’ev (Moskva) MSC: 12-02 12H05 12F10 12F20 12F12 PDF BibTeX XML Cite \textit{A. R. Magid}, Lectures on differential Galois theory. Providence, RI: AMS, American Mathematical Society (1994; Zbl 0855.12001) OpenURL
Ramis, Jean-Pierre About the solution of some inverse problems in differential Galois theory by Hamburger equations. (English) Zbl 0813.12005 Elworthy, K.D. (ed.) et al., Differential equations, dynamical systems, and control science. A Festschrift in Honor of Lawrence Markus. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 152, 277-299 (1994). Reviewer: E.V.Pankrat’ev (Moskva) MSC: 12H05 12F10 34A30 12F12 12F20 34M50 PDF BibTeX XML Cite \textit{J.-P. Ramis}, Lect. Notes Pure Appl. Math. 152, 277--299 (1994; Zbl 0813.12005) OpenURL
Singer, Michael F.; Ulmer, Felix On a third order differential equation whose differential Galois group is the simple group of 168 elements. (English) Zbl 0813.12002 Cohen, Gérard (ed.) et al., Applied algebra, algebraic algorithms and error-correcting codes. 10th International symposium, AAECC-10, San Juan de Puerto Rico, Puerto Rico, May 10-14, 1993. Proceedings. Berlin: Springer-Verlag. Lect. Notes Comput. Sci. 673, 316-324 (1993). Reviewer: E.V.Pankrat’ev (Moskva) MSC: 12H05 12F10 34A30 PDF BibTeX XML Cite \textit{M. F. Singer} and \textit{F. Ulmer}, Lect. Notes Comput. Sci. 673, 316--324 (1993; Zbl 0813.12002) OpenURL
Bertrand, Daniel Algebraic groups and linear differential equations. (Groupes algébriques et équations différentielles linéaires.) (French) Zbl 0813.12004 Séminaire Bourbaki, Vol. 1991/92. Exposés 745-759 (avec table par noms d’auteurs de 1948/49 à 1991/92). Paris: Société Mathématique de France, Astérisque. 206, 183-204 (Exp. No. 750) (1992). Reviewer: E.V.Pankrat’ev (Moskva) MSC: 12H05 12F10 34A30 12F20 PDF BibTeX XML Cite \textit{D. Bertrand}, in: Séminaire Bourbaki, volume 1991/92. Exposés 745-759 (avec table par noms d'auteurs de 1948/49 à 1991/92). Paris: Société Mathématique de France. 183--204 (Exp. No. 750) (1992; Zbl 0813.12004) Full Text: Numdam Link OpenURL
Fahim, Abdelmajid Extensions galoisiennes d’algèbres différentielles. (Galois extension of differential algebras). (French) Zbl 0748.12004 C. R. Acad. Sci., Paris, Sér. I 314, No. 1, 1-4 (1992). Reviewer: N.Radu (Bucureşti) MSC: 12H05 12H20 PDF BibTeX XML Cite \textit{A. Fahim}, C. R. Acad. Sci., Paris, Sér. I 314, No. 1, 1--4 (1992; Zbl 0748.12004) OpenURL
Martynyuk, A. N. The multiplicative integral and elementary solutions of some differential equations. (Russian) Zbl 0798.34010 Lupanov, O. B. (ed.) et al., Algebra, geometry and discrete mathematics in nonlinear problems. Moskva: Izdatel’stvo Moskovskogo Universiteta. 97-107 (1991). Reviewer: W.Müller (Berlin) MSC: 34A30 34A25 34M99 34A05 PDF BibTeX XML Cite \textit{A. N. Martynyuk}, in: Алгебра, геометрия и дискретная математика в нелинейных задачах. Moskva: Izdatel'stvo Moskovskogo Universiteta. 97--107 (1991; Zbl 0798.34010) OpenURL
Haraoka, Yoshishige G-primitive extensions for linear ordinary differential equations. (English) Zbl 0704.12008 Kumamoto J. Math. 3, 1-9 (1990). Reviewer: N.V.Grigorenko MSC: 12H05 12F05 PDF BibTeX XML Cite \textit{Y. Haraoka}, Kumamoto J. Math. 3, 1--9 (1990; Zbl 0704.12008) OpenURL
Takeuchi, Mitsuhiro A Hopf algebraic approach to the Picard-Vessiot theory. (English) Zbl 0669.16004 J. Algebra 122, No. 2, 481-509 (1989). Reviewer: E.J.Taft MSC: 16W30 12H05 34G10 16W20 PDF BibTeX XML Cite \textit{M. Takeuchi}, J. Algebra 122, No. 2, 481--509 (1989; Zbl 0669.16004) Full Text: DOI OpenURL
Okugawa, Kôtaro Differential algebra of nonzero characteristic. (English) Zbl 0757.12004 Lectures in Mathematics. Department of Mathematics, Kyoto University. 16. Tokyo: Kinokuniya Company Ltd. xi, 192 p. (1987). Reviewer: E.V.Pankrat’ev (Moskva) MSC: 12H05 12-02 13Nxx 12F10 PDF BibTeX XML Cite \textit{K. Okugawa}, Differential algebra of nonzero characteristic. Tokyo: Kinokuniya Company Ltd. (1987; Zbl 0757.12004) OpenURL
Ramis, Jean-Pierre Phénomène de Stokes et filtration Gevrey sur le groupe de Picard- Vessiot. (Stokes phenomena and Gevrey filtration on the Picard-Vessiot group). (French) Zbl 0593.12015 C. R. Acad. Sci., Paris, Sér. I 301, 165-167 (1985). Reviewer: M.F.Singer MSC: 12H05 34G10 PDF BibTeX XML Cite \textit{J.-P. Ramis}, C. R. Acad. Sci., Paris, Sér. I 301, 165--167 (1985; Zbl 0593.12015) OpenURL
Chudnovsky, D. V.; Chudnovsky, G. V. Rational approximations to solutions of linear differential equations. (English) Zbl 0516.12019 Proc. Natl. Acad. Sci. USA 80, 5158-5162 (1983). MSC: 12H20 12H05 11J68 11J61 41A21 PDF BibTeX XML Cite \textit{D. V. Chudnovsky} and \textit{G. V. Chudnovsky}, Proc. Natl. Acad. Sci. USA 80, 5158--5162 (1983; Zbl 0516.12019) Full Text: DOI OpenURL
Infante, Ronald P. On the inverse problem in difference Galois theory. (English) Zbl 0509.12024 Contemp. Math. 13, 349-352 (1982). MSC: 12H10 20G99 39A10 PDF BibTeX XML Cite \textit{R. P. Infante}, Contemp. Math. 13, 349--352 (1982; Zbl 0509.12024) Full Text: DOI OpenURL
Pommaret, Francois Théorie de Galois différentielle. (French) Zbl 0466.58030 C. R. Acad. Sci., Paris, Sér. I 292, 817-820 (1981). MSC: 58J99 12H20 58H05 13B10 11R32 13B05 37-XX PDF BibTeX XML Cite \textit{F. Pommaret}, C. R. Acad. Sci., Paris, Sér. I 292, 817--820 (1981; Zbl 0466.58030) OpenURL
Tretkoff, Carol; Tretkoff, Marvin Solution of the inverse problem of differential Galois theory in the classical case. (English) Zbl 0423.12021 Am. J. Math. 101, 1327-1332 (1979). MSC: 12H05 12F10 PDF BibTeX XML Cite \textit{C. Tretkoff} and \textit{M. Tretkoff}, Am. J. Math. 101, 1327--1332 (1979; Zbl 0423.12021) Full Text: DOI OpenURL
Grigorenko, N. V. On Picard-Vessiot extensions of differential fields. (English) Zbl 0413.12025 Math. USSR, Sb. 34, 701-706 (1978). MSC: 12H20 12H05 PDF BibTeX XML Cite \textit{N. V. Grigorenko}, Math. USSR, Sb. 34, 701--706 (1978; Zbl 0413.12025) Full Text: DOI OpenURL