Guterman, Alexander; Zhilina, Svetlana On the lengths of descendingly flexible and descendingly alternative algebras. arXiv:2312.03170 Preprint, arXiv:2312.03170 [math.RA] (2023). MSC: 15A03 17A20 17A30 17D05 BibTeX Cite \textit{A. Guterman} and \textit{S. Zhilina}, ``On the lengths of descendingly flexible and descendingly alternative algebras'', Preprint, arXiv:2312.03170 [math.RA] (2023) Full Text: arXiv OA License
Yahaghi, Bamdad R. Extensions of the fundamental theorem of algebra. arXiv:2203.14689 Preprint, arXiv:2203.14689 [math.RA] (2022). MSC: 46H70 13J30 15A18 15A60 16W99 17D05 BibTeX Cite \textit{B. R. Yahaghi}, ``Extensions of the fundamental theorem of algebra'', Preprint, arXiv:2203.14689 [math.RA] (2022) Full Text: arXiv OA License
Berman, Abraham; Borer, Franziska; Hungerbühler, Norbert Lights Out on graphs. (English) Zbl 1502.05162 Math. Semesterber. 68, No. 2, 237-255 (2021). Reviewer: V. Yegnanarayanan (Chennai) MSC: 05C57 15A99 15B33 68Q17 91A43 PDFBibTeX XMLCite \textit{A. Berman} et al., Math. Semesterber. 68, No. 2, 237--255 (2021; Zbl 1502.05162) Full Text: DOI arXiv
Bartl, David A discrete variant of Farkas’ lemma and related results. (English) Zbl 1477.15013 Optimization 70, No. 9, 2031-2060 (2021). MSC: 15A39 06F25 06F20 PDFBibTeX XMLCite \textit{D. Bartl}, Optimization 70, No. 9, 2031--2060 (2021; Zbl 1477.15013) Full Text: DOI
Chapman, Adam Polynomial equations over octonion algebras. (English) Zbl 1450.17012 J. Algebra Appl. 19, No. 6, Article ID 2050102, 10 p. (2020). Reviewer: Ivan Kaygorodov (Novosibirsk) MSC: 17D05 15A18 15B33 PDFBibTeX XMLCite \textit{A. Chapman}, J. Algebra Appl. 19, No. 6, Article ID 2050102, 10 p. (2020; Zbl 1450.17012) Full Text: DOI arXiv
Chapman, Adam; Vishne, Uzi The alternative Clifford algebra of a ternary quadratic form. (English) Zbl 1452.17032 Commun. Algebra 47, No. 10, 3987-3994 (2019). Reviewer: Alberto Elduque (Zaragoza) MSC: 17D05 11E04 11E81 15A66 PDFBibTeX XMLCite \textit{A. Chapman} and \textit{U. Vishne}, Commun. Algebra 47, No. 10, 3987--3994 (2019; Zbl 1452.17032) Full Text: DOI arXiv
Chanyal, B. C. Octonion generalization of Pauli and Dirac matrices. (English) Zbl 1393.17051 Int. J. Geom. Methods Mod. Phys. 12, No. 1, Article ID 1550007, 24 p. (2015). Reviewer: Dmitry Shirokov (Moscow) MSC: 17D05 15A66 15B99 81R20 PDFBibTeX XMLCite \textit{B. C. Chanyal}, Int. J. Geom. Methods Mod. Phys. 12, No. 1, Article ID 1550007, 24 p. (2015; Zbl 1393.17051) Full Text: DOI
Tian, Yongge Solving some linear equations over alternative rings. (English) Zbl 1201.17019 Result. Math. 58, No. 3-4, 355-364 (2010). Reviewer: K. C. Sivakumar (Chennai) MSC: 17D05 15A09 17A30 PDFBibTeX XMLCite \textit{Y. Tian}, Result. Math. 58, No. 3--4, 355--364 (2010; Zbl 1201.17019) Full Text: DOI
Wang, Minghui; Wei, Musheng; Feng, Yan An iterative algorithm for least squares problem in quaternionic quantum theory. (English) Zbl 1197.81138 Comput. Phys. Commun. 179, No. 4, 203-207 (2008). MSC: 81Q65 15A24 15B33 PDFBibTeX XMLCite \textit{M. Wang} et al., Comput. Phys. Commun. 179, No. 4, 203--207 (2008; Zbl 1197.81138) Full Text: DOI
Lam, T. Y.; Swan, R. G. Sums of alternating matrices and invertible matrices. (English) Zbl 1114.15012 Huynh, Dinh V. (ed.) et al., Algebra and its applications. Proceedings of the international conference, Athens, OH, USA, March 22–26, 2005. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3842-3/pbk). Contemporary Mathematics 419, 201-211 (2006). MSC: 15B33 15B57 16L30 16K99 16K20 PDFBibTeX XMLCite \textit{T. Y. Lam} and \textit{R. G. Swan}, Contemp. Math. 419, 201--211 (2006; Zbl 1114.15012)
Giraldo Vergara, Carmen Rosa; Brochero Martínez, Fabio Enrique Zorn’s matrices and finite index subloops. (English) Zbl 1102.20050 Commun. Algebra 33, No. 10, 3691-3698 (2005). Reviewer: Huberta Lausch (Grafing) MSC: 20N05 20H05 17D05 15A30 PDFBibTeX XMLCite \textit{C. R. Giraldo Vergara} and \textit{F. E. Brochero Martínez}, Commun. Algebra 33, No. 10, 3691--3698 (2005; Zbl 1102.20050) Full Text: DOI arXiv
Goldberg, Moshe Stable norms –from theory to applications and back. (English) Zbl 1078.15022 Linear Algebra Appl. 404, 223-250 (2005). Reviewer: Alexey Alimov (Moskva) MSC: 15A60 17A05 65M06 65M12 35K15 PDFBibTeX XMLCite \textit{M. Goldberg}, Linear Algebra Appl. 404, 223--250 (2005; Zbl 1078.15022) Full Text: DOI
Wu, Yan; Nan, Jizhu Some Anzahl theorems of alternate matrices over \(Z/p^kZ\) and its application. (Chinese. English summary) Zbl 1072.15024 Acta Math. Sci., Ser. A, Chin. Ed. 24, No. 3, 319-328 (2004). MSC: 15B33 15A21 15B57 PDFBibTeX XMLCite \textit{Y. Wu} and \textit{J. Nan}, Acta Math. Sci., Ser. A, Chin. Ed. 24, No. 3, 319--328 (2004; Zbl 1072.15024)
Dieterich, Ernst Eight-dimensional real quadratic division algebras. (English) Zbl 0982.17001 AMA, Algebra Montp. Announc. 2000, No. 1, Paper No. 2, 5 p. (2000). Reviewer: Elena Brožíková (Praha) MSC: 17A35 15A21 15A23 17A05 PDFBibTeX XMLCite \textit{E. Dieterich}, AMA, Algebra Montp. Announc. 2000, No. 1, Paper No. 2, 5 p. (2000; Zbl 0982.17001) Full Text: EuDML EMIS
Dieterich, Ernst On the classification of real four-dimensional division algebras. (Zur Klassifikation vierdimensionaler reeller Divisionsalgebren.) (German) Zbl 0915.17002 Math. Nachr. 194, 13-22 (1998). Reviewer: B.Fauser (Tübingen) MSC: 17A35 17A05 15A63 PDFBibTeX XMLCite \textit{E. Dieterich}, Math. Nachr. 194, 13--22 (1998; Zbl 0915.17002) Full Text: DOI
Bourbaki, Nicolas Elements of mathematics. Algebra I. Chapters 1–3. Transl. from the French. Softcover edition of the 2nd printing 1989. (English) Zbl 0904.00001 Berlin: Springer. xxiii, 709 p. (1998). Reviewer: V.Drensky (Sofia) MSC: 00A05 12-01 15-01 20-01 16-01 17-01 15A69 15A72 15A75 15A78 17D05 20E05 20F16 PDFBibTeX XMLCite \textit{N. Bourbaki}, Elements of mathematics. Algebra I. Chapters 1--3. Transl. from the French. Softcover edition of the 2nd printing 1989. Berlin: Springer (1998; Zbl 0904.00001)
Dzierzgowski, D.; Tignol, J.-P. Characterization of quaternion and octonion algebras of characteristic 2 by their central square elements. (Une caractérisation des algèbres de quaternions et d’octonions en caractéristique 2 par leurs éléments de carré central.) (French) Zbl 0840.17029 Rapp., Sémin. Math., Louvain, Nouv. Sér. 221-236, 137-165 (1993). Reviewer: A.H.Boers (Rijswijk) MSC: 17D05 16S99 15B33 PDFBibTeX XMLCite \textit{D. Dzierzgowski} and \textit{J. P. Tignol}, Rapp., Sémin. Math., Louvain, Nouv. Sér. 221--236, 137--165 (1993; Zbl 0840.17029)
Lü, Haibo A kind of Hamilton algebra. (Chinese. English summary) Zbl 0819.16016 J. Math. Res. Expo. 12, No. 3, 375-378 (1992). Reviewer: K.-P.Shum (Hongkong) MSC: 16K40 17D05 15A03 17A60 PDFBibTeX XMLCite \textit{H. Lü}, J. Math. Res. Expo. 12, No. 3, 375--378 (1992; Zbl 0819.16016)
Dutilleul, P.; Tignol, J.-P. Une caractérisation des algèbres de quaternions et d’octonions par leurs éléments de carré central. (A characterization of quaternion and octonion algebras by their central square element). (French) Zbl 0715.17031 Bull. Soc. Math. Belg., Sér. B 42, No. 3, 369-378 (1990). Reviewer: A.H.Boers MSC: 17D05 15A63 PDFBibTeX XMLCite \textit{P. Dutilleul} and \textit{J. P. Tignol}, Bull. Soc. Math. Belg., Sér. B 42, No. 3, 369--378 (1990; Zbl 0715.17031)
Neumann, Alf Automorphismen von Cayleyalgebren über algebraischen Erweiterungen endlicher Körper ungerader Charakteristik. (Automorphisms of Cayley algebras over algebraic extensions of finite fields of odd characteristic). (German) Zbl 0714.17002 Result. Math. 18, No. 3-4, 314-319 (1990). Reviewer: Huberta Lausch MSC: 17A36 15A23 17D05 PDFBibTeX XMLCite \textit{A. Neumann}, Result. Math. 18, No. 3--4, 314--319 (1990; Zbl 0714.17002) Full Text: DOI
Kantor, I. L.; Solodovnikov, A. S. [Shenitzer, A.] Hypercomplex numbers. An elementary introduction to algebras. Transl. by A. Shenitzer. (English) Zbl 0669.17001 New York etc.: Springer-Verlag. x, 169 p. DM 78.00 (1989). Reviewer: A.H.Boers MSC: 17-01 15-01 17A35 16Kxx 17D05 16P10 30G35 PDFBibTeX XMLCite \textit{I. L. Kantor} and \textit{A. S. Solodovnikov}, Hypercomplex numbers. An elementary introduction to algebras. Transl. by A. Shenitzer. New York etc.: Springer-Verlag (1989; Zbl 0669.17001)
Lambert, D.; Kibler, M. An algebraic and geometric approach to non-bijective quadratic transformations. (English) Zbl 0659.15030 J. Phys. A 21, No. 2, 307-343 (1988). Reviewer: T.Nôno MSC: 15A66 17D05 PDFBibTeX XMLCite \textit{D. Lambert} and \textit{M. Kibler}, J. Phys. A, Math. Gen. 21, No. 2, 307--343 (1988; Zbl 0659.15030) Full Text: DOI
Cohen, Arjeh M.; Helminck, Aloysius G. Trilinear alternating forms on a vector space of dimension 7. (English) Zbl 0646.15019 Commun. Algebra 16, No. 1, 1-25 (1988). Reviewer: A.H.Boers MSC: 15A63 11E76 20G15 17D05 PDFBibTeX XMLCite \textit{A. M. Cohen} and \textit{A. G. Helminck}, Commun. Algebra 16, No. 1, 1--25 (1988; Zbl 0646.15019) Full Text: DOI Link
Küting, Brigitte Kompositionsalgebren über rationalen Funktionenkörpern. (Composition algebras over rational function fields). (German) Zbl 0647.17003 Hagen (FRG): Fernuniv. Hagen, Fachbereich Mathematik und Informatik, Diss. 175 S. (1987). Reviewer: R.Carles MSC: 17A75 17D05 15A63 PDFBibTeX XML
Waterhouse, William C. On linear transformations preserving rank one matrices over commutative rings. (English) Zbl 0566.15005 Linear Multilinear Algebra 17, 101-106 (1985). Reviewer: V.Perić MSC: 15A15 15B33 15A63 PDFBibTeX XMLCite \textit{W. C. Waterhouse}, Linear Multilinear Algebra 17, 101--106 (1985; Zbl 0566.15005) Full Text: DOI
Eganova, I. A.; Shirokov, M. I. Orthomatrices and octonions. (English) Zbl 0555.17005 Rep. Math. Phys. 20, 1-10 (1984). Reviewer: K. Yamaguti MSC: 17D05 15A30 15B57 PDFBibTeX XMLCite \textit{I. A. Eganova} and \textit{M. I. Shirokov}, Rep. Math. Phys. 20, 1--10 (1984; Zbl 0555.17005) Full Text: DOI
Wene, G. P. A construction relating Clifford algebras and Cayley-Dickson algebras. (English) Zbl 0555.15013 J. Math. Phys. 25, 2351-2353 (1984). Reviewer: A.H.Boers MSC: 15A66 17A35 15A90 17A05 17A20 17D05 PDFBibTeX XMLCite \textit{G. P. Wene}, J. Math. Phys. 25, 2351--2353 (1984; Zbl 0555.15013) Full Text: DOI
Adamushko, N. N.; Kuznetsova, T. A. Simple, quasi-simple and bi-quasi-simple algebras of vector-matrices. (Russian) Zbl 0471.17007 Geom. Sb. 19, 24-28 (1978). MSC: 17D05 15B33 17D99 PDFBibTeX XMLCite \textit{N. N. Adamushko} and \textit{T. A. Kuznetsova}, Geom. Sb. 19, 24--28 (1978; Zbl 0471.17007)
Hahn, Alexander J. Cayley algebras and the isomorphisms of the orthogonal groups over arithmetic and local domains. (English) Zbl 0363.20034 J. Algebra 45, 210-246 (1977). MSC: 20G05 20E36 17D05 15A63 PDFBibTeX XMLCite \textit{A. J. Hahn}, J. Algebra 45, 210--246 (1977; Zbl 0363.20034) Full Text: DOI
Hahn, Alexander Cayley algebras and the automorphisms of \(PO'_8(V)\) and \(P\Omega_8(V)\). (English) Zbl 0363.20033 Am. J. Math. 98, 953-987 (1976). MSC: 20G05 17D05 15A63 20E36 PDFBibTeX XMLCite \textit{A. Hahn}, Am. J. Math. 98, 953--987 (1976; Zbl 0363.20033) Full Text: DOI
Hein, W. A connection between Lie algebras of type \(F_4\) and Cayley algebras. (English) Zbl 0361.17006 Nederl. Akad. Wet., Proc., Ser. A 79, 419-425 (1976). MSC: 17D05 17B25 15A66 PDFBibTeX XMLCite \textit{W. Hein}, Nederl. Akad. Wet., Proc., Ser. A 79, 419--425 (1976; Zbl 0361.17006)
Epp, Susanna Samuels The Brandt condition in Cayley algebras. (English) Zbl 0346.17018 J. Algebra 38, 213-224 (1976). MSC: 17D05 11E16 15A63 11R52 PDFBibTeX XMLCite \textit{S. S. Epp}, J. Algebra 38, 213--224 (1976; Zbl 0346.17018) Full Text: DOI
Legrand, D. Formes quadratiques et algèbres quadratiques. (French) Zbl 0357.17003 Ann. Sci. Univ. Clermont 54, Math. 10, 45-107 (1975). MSC: 17A99 17D05 15A63 PDFBibTeX XMLCite \textit{D. Legrand}, Ann. Sci. Univ. Clermont-Ferrand II, Math. 54(10), 45--107 (1975; Zbl 0357.17003) Full Text: Numdam EuDML
Petersson, Holger P. Composition algebras over a field with a discrete valuation. (English) Zbl 0291.17013 J. Algebra 29, 414-426 (1974). Reviewer: Witold Więsław (Wrocław) MSC: 17A75 17D05 12J99 15A63 PDFBibTeX XMLCite \textit{H. P. Petersson}, J. Algebra 29, 414--426 (1974; Zbl 0291.17013) Full Text: DOI
Kantor, I. L.; Solodovnikov, A. S. Hypercomplex numbers. (Giperkompleksnye chisla). (Russian) Zbl 0669.17002 Moskva: Nauka. 144 p. (1973). MSC: 17-01 15-01 17A35 16Kxx 17D05 16P10 30G35 PDFBibTeX XML
Legrand, Denise Formes quadratiques multiplicatives sur une Q-algèbre. (French) Zbl 0267.15008 C. R. Acad. Sci., Paris, Sér. A 273, 548-550 (1971). MSC: 15A63 17D05 17A05 PDFBibTeX XMLCite \textit{D. Legrand}, C. R. Acad. Sci., Paris, Sér. A 273, 548--550 (1971; Zbl 0267.15008)