Bavula, V. V. Classifications of prime ideals and simple modules of the Weyl algebra \(A_1\) in prime characteristic. (English) Zbl 07713966 Tokyo J. Math. 46, No. 1, 161-191 (2023). MSC: 16D70 16D60 16K20 16S36 16S32 16D25 16W20 PDFBibTeX XMLCite \textit{V. V. Bavula}, Tokyo J. Math. 46, No. 1, 161--191 (2023; Zbl 07713966) Full Text: DOI Link
Bavula, Volodymyr; Hakami, K. Rings of differential operators on singular generalized multi-cusp algebras. arXiv:2312.17303 Preprint, arXiv:2312.17303 [math.RA] (2023). MSC: 16S32 16E10 16E05 16D60 16P40 16S35 16S15 16P50 16P90 16D30 BibTeX Cite \textit{V. Bavula} and \textit{K. Hakami}, ``Rings of differential operators on singular generalized multi-cusp algebras'', Preprint, arXiv:2312.17303 [math.RA] (2023) Full Text: arXiv OA License
Bavula, Volodymyr Classifications of prime ideals and simple modules of the quantum Weyl algebra \(A_1(q)\) (\(q\) is a root of unity). arXiv:2312.17302 Preprint, arXiv:2312.17302 [math.RA] (2023). MSC: 16D70 16D60 16K20 16S36 16S32 16D25 16W20 BibTeX Cite \textit{V. Bavula}, ``Classifications of prime ideals and simple modules of the quantum Weyl algebra $A_1(q)$ ($q$ is a root of unity)'', Preprint, arXiv:2312.17302 [math.RA] (2023) Full Text: arXiv OA License
Bavula, Volodymyr; Khabyah, A. Al Bi-quadratic algebras on 3 generators with PBW: class II.1. arXiv:2312.17182 Preprint, arXiv:2312.17182 [math.RA] (2023). MSC: 16D60 16W20 16S37 16P20 16U70 16S36 16D25 16E10 16S99 16D60 BibTeX Cite \textit{V. Bavula} and \textit{A. A. Khabyah}, ``Bi-quadratic algebras on 3 generators with PBW: class II.1'', Preprint, arXiv:2312.17182 [math.RA] (2023) Full Text: arXiv OA License
Bavula, V. V.; Bekkert, V.; Futorny, V. Explicit description of generalized weight modules of the algebra of polynomial integro-differential operators \(\mathbb{I}_n\). (English) Zbl 1509.16007 Asian J. Math. 25, No. 5, 727-756 (2021). Reviewer: Blas Torrecillas (Almería) MSC: 16D60 16D70 16G60 16P50 16U20 PDFBibTeX XMLCite \textit{V. V. Bavula} et al., Asian J. Math. 25, No. 5, 727--756 (2021; Zbl 1509.16007) Full Text: DOI arXiv
Bavula, V.; Lu, T. The prime spectrum of the universal enveloping algebra of the 1-spatial ageing algebra and of \(U(\mathfrak{gl}_2)\). (English) Zbl 1490.17017 Algebra Discrete Math. 31, No. 1, 1-16 (2021). Reviewer: Victor Petrogradsky (Brasília) MSC: 17B35 16D25 16D60 16D70 16P50 PDFBibTeX XMLCite \textit{V. Bavula} and \textit{T. Lu}, Algebra Discrete Math. 31, No. 1, 1--16 (2021; Zbl 1490.17017) Full Text: DOI
Bavula, V. V. Isomorphism problems and groups of automorphisms for Ore extensions \(K[x][y; f\frac{d}{dx} ]\) (prime characteristic). arXiv:2107.09977 Preprint, arXiv:2107.09977 [math.RA] (2021). MSC: 16D60 13N10 16S32 16P90 16U20 BibTeX Cite \textit{V. V. Bavula}, ``Isomorphism problems and groups of automorphisms for Ore extensions $K[x][y; f\frac{d}{dx} ]$ (prime characteristic)'', Preprint, arXiv:2107.09977 [math.RA] (2021) Full Text: arXiv OA License
Bavula, V. V. The Poisson enveloping algebra and the algebra of Poisson differential operators of a generalized Weyl Poisson algebra. arXiv:2107.00944 Preprint, arXiv:2107.00944 [math.RA] (2021). MSC: 17B63 17B65 17B20 16S32 16D30 14F10 16P90 13N15 14J17 14B05 BibTeX Cite \textit{V. V. Bavula}, ``The Poisson enveloping algebra and the algebra of Poisson differential operators of a generalized Weyl Poisson algebra'', Preprint, arXiv:2107.00944 [math.RA] (2021) Full Text: arXiv OA License
Bavula, V. V. The PBW Theorem and simplicity criteria for the Poisson enveloping algebra and the algebra of Poisson differential operators. arXiv:2107.00321 Preprint, arXiv:2107.00321 [math.RA] (2021). MSC: 17B63 17B65 17B20 13N05 13N15 16D30 16S32 16P90 BibTeX Cite \textit{V. V. Bavula}, ``The PBW Theorem and simplicity criteria for the Poisson enveloping algebra and the algebra of Poisson differential operators'', Preprint, arXiv:2107.00321 [math.RA] (2021) Full Text: arXiv OA License
Bavula, Volodymyr V.; Lu, Tao The prime ideals and simple modules of the universal enveloping algebra \(U(\mathfrak{b}\ltimes V_2)\). (English) Zbl 1477.17055 Glasg. Math. J. 62, No. S1, S77-S98 (2020). MSC: 17B10 17B35 16D25 16D60 16D70 16P50 PDFBibTeX XMLCite \textit{V. V. Bavula} and \textit{T. Lu}, Glasg. Math. J. 62, No. S1, S77--S98 (2020; Zbl 1477.17055) Full Text: DOI
Bavula, V. V. Generalized Weyl algebras and diskew polynomial rings. (English) Zbl 1464.16018 J. Algebra Appl. 19, No. 10, Article ID 2050194, 43 p. (2020). MSC: 16S36 16D25 16S30 16D60 16P40 PDFBibTeX XMLCite \textit{V. V. Bavula}, J. Algebra Appl. 19, No. 10, Article ID 2050194, 43 p. (2020; Zbl 1464.16018) Full Text: DOI arXiv
Bavula, V. V. Classification of simple modules of the Ore extension \(K[X][Y; f\frac{d}{dX}]\). (English) Zbl 1462.16027 Math. Comput. Sci. 14, No. 2, 317-325 (2020). MSC: 16S36 16D60 13N10 16S32 PDFBibTeX XMLCite \textit{V. V. Bavula}, Math. Comput. Sci. 14, No. 2, 317--325 (2020; Zbl 1462.16027) Full Text: DOI
Bavula, V. V.; Lu, Tao The prime ideals and simple weight modules of the algebra \(U(\mathfrak{b}\ltimes V_3)\). (English) Zbl 1455.17006 Leroy, André (ed.) et al., Rings, modules and codes. Fifth international conference on noncommutative rings and their applications, University of Artois, Lens, France, June 12–15, 2017. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 727, 49-70 (2019). MSC: 17B10 16D25 16D60 16D70 16P50 PDFBibTeX XMLCite \textit{V. V. Bavula} and \textit{T. Lu}, Contemp. Math. 727, 49--70 (2019; Zbl 1455.17006) Full Text: DOI
Bavula, Volodymyr; Futorny, Vyacheslav Rings of invariants of finite groups when the bad primes exist. (English) Zbl 1470.16074 Commun. Algebra 47, No. 10, 4114-4124 (2019). MSC: 16W22 16N20 16N60 20C05 PDFBibTeX XMLCite \textit{V. Bavula} and \textit{V. Futorny}, Commun. Algebra 47, No. 10, 4114--4124 (2019; Zbl 1470.16074) Full Text: DOI arXiv Link
Bavula, V. V.; Lu, T. The universal enveloping algebra of the Schrödinger algebra and its prime spectrum. (English) Zbl 1472.17023 Can. Math. Bull. 61, No. 4, 688-703 (2018). MSC: 17B10 16D25 16D60 16D70 16P50 PDFBibTeX XMLCite \textit{V. V. Bavula} and \textit{T. Lu}, Can. Math. Bull. 61, No. 4, 688--703 (2018; Zbl 1472.17023) Full Text: Link
Bavula, Vladimir V.; Lu, Tao The prime spectrum of the algebra \(\mathbb{K}_q[X,Y] \rtimes U_q(\mathfrak{sl}_2)\) and a classification of simple weight modules. (English) Zbl 1408.17003 J. Noncommut. Geom. 12, No. 3, 889-946 (2018). Reviewer: Victor Petrogradsky (Brasilia) MSC: 17B10 17B35 16D25 16D60 16D70 16P50 PDFBibTeX XMLCite \textit{V. V. Bavula} and \textit{T. Lu}, J. Noncommut. Geom. 12, No. 3, 889--946 (2018; Zbl 1408.17003) Full Text: DOI
Bavula, V. V.; Lu, Tao Classification of simple weight modules over the Schrödinger algebra. (English) Zbl 1426.17005 Can. Math. Bull. 61, No. 1, 16-39 (2018). MSC: 17B10 17B20 17B35 16E10 16P90 16P40 16P50 PDFBibTeX XMLCite \textit{V. V. Bavula} and \textit{T. Lu}, Can. Math. Bull. 61, No. 1, 16--39 (2018; Zbl 1426.17005) Full Text: DOI
Bavula, V. V.; Lu, T. Torsion simple modules over the quantum spatial ageing algebra. (English) Zbl 1378.16033 Commun. Algebra 45, No. 10, 4166-4189 (2017). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 16S36 16D60 16D70 PDFBibTeX XMLCite \textit{V. V. Bavula} and \textit{T. Lu}, Commun. Algebra 45, No. 10, 4166--4189 (2017; Zbl 1378.16033) Full Text: DOI Link
Bavula, V. V.; Lu, Tao The prime spectrum and simple modules over the quantum spatial ageing algebra. (English) Zbl 1410.17013 Algebr. Represent. Theory 19, No. 5, 1109-1133 (2016). MSC: 17B37 16S36 16D60 16G99 16P50 PDFBibTeX XMLCite \textit{V. V. Bavula} and \textit{T. Lu}, Algebr. Represent. Theory 19, No. 5, 1109--1133 (2016; Zbl 1410.17013) Full Text: DOI arXiv
Bavula, V. V. The algebra of polynomial integro-differential operators is a holonomic bimodule over the subalgebra of polynomial differential operators. (English) Zbl 1305.16019 Algebr. Represent. Theory 17, No. 1, 275-288 (2014). Reviewer: Vyacheslav A. Artamonov (Moskva) MSC: 16S32 16D60 32C38 PDFBibTeX XMLCite \textit{V. V. Bavula}, Algebr. Represent. Theory 17, No. 1, 275--288 (2014; Zbl 1305.16019) Full Text: DOI arXiv
Bavula, V. V. The algebra of integro-differential operators on an affine line and its modules. (English) Zbl 1272.16027 J. Pure Appl. Algebra 217, No. 3, 495-529 (2013). Reviewer: Vyacheslav A. Artamonov (Moskva) MSC: 16S32 16D60 16S36 PDFBibTeX XMLCite \textit{V. V. Bavula}, J. Pure Appl. Algebra 217, No. 3, 495--529 (2013; Zbl 1272.16027) Full Text: DOI arXiv
Bavula, V. V.; Hinchcliffe, V. Morita invariance of the filter dimension and of the inequality of Bernstein. (English) Zbl 1178.16003 Algebr. Represent. Theory 11, No. 5, 497-504 (2008). Reviewer: Vyacheslav A. Artamonov (Moskva) MSC: 16D60 16P90 16E10 16W60 16D90 16S32 16D30 16W70 PDFBibTeX XMLCite \textit{V. V. Bavula} and \textit{V. Hinchcliffe}, Algebr. Represent. Theory 11, No. 5, 497--504 (2008; Zbl 1178.16003) Full Text: DOI arXiv
Bavula, V. V. The Carlitz algebras. (English) Zbl 1140.16009 J. Pure Appl. Algebra 212, No. 5, 1175-1186 (2008). Reviewer: Vyacheslav A. Artamonov (Moskva) MSC: 16S32 16D60 16W60 16P60 PDFBibTeX XMLCite \textit{V. V. Bavula}, J. Pure Appl. Algebra 212, No. 5, 1175--1186 (2008; Zbl 1140.16009) Full Text: DOI arXiv
Bavula, V. Filter dimension. (English) Zbl 1211.16017 Hazewinkel, M. (ed.), Handbook of algebra. Volume 4. Amsterdam: Elsevier/North-Holland (ISBN 978-0-444-52213-9/hbk). Handbook of Algebra 4, 77-105 (2006). Reviewer: Florin Nicolae (Berlin) MSC: 16P90 16-02 16E10 16D60 16W60 16S32 PDFBibTeX XMLCite \textit{V. Bavula}, Handb. Algebra 4, 77--105 (2006; Zbl 1211.16017) Full Text: DOI arXiv
Bavula, V.; Van Oystaeyen, F. Simple modules of the Witten-Woronowicz algebra. (English) Zbl 1047.16001 J. Algebra 271, No. 2, 827-845 (2004). Reviewer: Vyacheslav A. Artamonov (Moskva) MSC: 16D60 16S36 16S80 PDFBibTeX XMLCite \textit{V. Bavula} and \textit{F. Van Oystaeyen}, J. Algebra 271, No. 2, 827--845 (2004; Zbl 1047.16001) Full Text: DOI
Bavula, V.; Van Oystaeyen, F. Simple holonomic modules over rings of differential operators with regular coefficients of Krull dimension 2. (English) Zbl 1017.16016 Trans. Am. Math. Soc. 353, No. 6, 2193-2214 (2001). MSC: 16S32 16P60 16D60 PDFBibTeX XMLCite \textit{V. Bavula} and \textit{F. Van Oystaeyen}, Trans. Am. Math. Soc. 353, No. 6, 2193--2214 (2001; Zbl 1017.16016) Full Text: DOI
Bavula, V.; van Oystaeyen, F. The simple modules of the Lie superalgebra \(osp (1,2)\). (English) Zbl 1006.17009 J. Pure Appl. Algebra 150, No. 1, 41-52 (2000). MSC: 17B10 17B20 PDFBibTeX XMLCite \textit{V. Bavula} and \textit{F. van Oystaeyen}, J. Pure Appl. Algebra 150, No. 1, 41--52 (2000; Zbl 1006.17009) Full Text: DOI
Bavula, V. V. The extension group of the simple modules over the first Weyl algebra. (English) Zbl 1021.16002 Bull. Lond. Math. Soc. 32, No. 2, 182-190 (2000). MSC: 16E30 16S36 16D60 PDFBibTeX XMLCite \textit{V. V. Bavula}, Bull. Lond. Math. Soc. 32, No. 2, 182--190 (2000; Zbl 1021.16002) Full Text: DOI
Bavula, V.; Van Oystaeyen, F. Simple holonomic modules over the second Weyl algebra \(A_2\). (English) Zbl 0947.16008 Adv. Math. 150, No. 1, 80-116 (2000). Reviewer: T.H.Lenagan (Edinburgh) MSC: 16P40 16D30 16D60 16P90 16S32 16S36 PDFBibTeX XMLCite \textit{V. Bavula} and \textit{F. Van Oystaeyen}, Adv. Math. 150, No. 1, 80--116 (2000; Zbl 0947.16008) Full Text: DOI
Bavula, V. V.; Lenagan, T. H. A Bernstein-Gabber-Joseph theorem for affine algebras. (English) Zbl 0938.16013 Proc. Edinb. Math. Soc., II. Ser. 42, No. 2, 311-332 (1999). Reviewer: G.Krause (Winnipeg) MSC: 16P90 16P40 16D60 16S32 PDFBibTeX XMLCite \textit{V. V. Bavula} and \textit{T. H. Lenagan}, Proc. Edinb. Math. Soc., II. Ser. 42, No. 2, 311--332 (1999; Zbl 0938.16013) Full Text: DOI
Bavula, V. The simple modules of the Ore extensions with coefficients from a Dedekind ring. (English) Zbl 0944.16001 Commun. Algebra 27, No. 6, 2665-2699 (1999). Reviewer: G.Krause (Winnipeg) MSC: 16D60 16S36 13F05 13F07 PDFBibTeX XMLCite \textit{V. Bavula}, Commun. Algebra 27, No. 6, 2665--2699 (1999; Zbl 0944.16001) Full Text: DOI
Bavula, V.; Van Oystaeyen, F. The simple modules of certain generalized crossed products. (English) Zbl 0927.16002 J. Algebra 194, No. 2, 521-566 (1997). Reviewer: D.A.Jordan (Sheffield) MSC: 16D60 16S35 16S36 16W50 PDFBibTeX XMLCite \textit{V. Bavula} and \textit{F. Van Oystaeyen}, J. Algebra 194, No. 2, 521--566 (1997; Zbl 0927.16002) Full Text: DOI Link
Bavula, Vladimir Filter dimension of algebras and modules, a simplicity criterion of generalized Weyl algebras. (English) Zbl 0855.16005 Commun. Algebra 24, No. 6, 1971-1992 (1996). Reviewer: G.Krause (Winnipeg) MSC: 16D60 16P90 16E10 16W60 17B35 16P40 16S32 PDFBibTeX XMLCite \textit{V. Bavula}, Commun. Algebra 24, No. 6, 1971--1992 (1996; Zbl 0855.16005) Full Text: DOI
Bavula, V. V. Classification of modules of Gel’fand-Kirillov dimension \(n\) and multiplicity \(1\) over the Weyl algebra \(A_n\). (English. Russian original) Zbl 0906.16010 Izv. Math. 60, No. 5, 877-885 (1996); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 60, No. 5, 3-12 (1996). Reviewer: A.Marcus (Cluj-Napoca) MSC: 16S32 16D60 16W60 16P90 PDFBibTeX XMLCite \textit{V. V. Bavula}, Izv. Math. 60, No. 5, 877--885 (1996; Zbl 0906.16010); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 60, No. 5, 3--12 (1996) Full Text: DOI
Bavula, Vladimir Module structure of the tensor product of simple algebras of Krull dimension \(1\). (English) Zbl 0880.16003 An. Științ. Univ. “Ovidius” Constanța, Ser. Mat. 4, No. 2, 7-21 (1996). Reviewer: T.Albu (Bucureşti) MSC: 16D60 16P20 16S32 16K20 16P70 16D25 PDFBibTeX XMLCite \textit{V. Bavula}, An. Științ. Univ. ``Ovidius'' Constanța, Ser. Mat. 4, No. 2, 7--21 (1996; Zbl 0880.16003)
Bavula, Vladimir Each Schurian algebra is tensor-simple. (English) Zbl 0832.16001 Commun. Algebra 23, No. 4, 1363-1367 (1995). Reviewer: H.Meltzer (Chemnitz) MSC: 16D90 16D60 15A72 PDFBibTeX XMLCite \textit{V. Bavula}, Commun. Algebra 23, No. 4, 1363--1367 (1995; Zbl 0832.16001) Full Text: DOI
Bavula, V. V. Extreme modules over the Weyl algebra \(A_ n\). (English. Russian original) Zbl 0829.16005 Ukr. Math. J. 45, No. 9, 1327-1338 (1993); translation from Ukr. Mat. Zh. 45, No. 9, 1187-1197 (1993). MSC: 16D60 16S32 17B20 16W60 17B35 16S30 PDFBibTeX XMLCite \textit{V. V. Bavula}, Ukr. Math. J. 45, No. 9, 1187--1197 (1993; Zbl 0829.16005); translation from Ukr. Mat. Zh. 45, No. 9, 1187--1197 (1993) Full Text: DOI
Bavula, V. V. Generalized Weyl algebras and their representations. (English. Russian original) Zbl 0807.16027 St. Petersbg. Math. J. 4, No. 1, 71-92 (1993); translation from Algebra Anal. 4, No. 1, 75-97 (1992). MSC: 16S30 16P60 16D60 17B35 16D25 16E30 PDFBibTeX XMLCite \textit{V. V. Bavula}, St. Petersbg. Math. J. 4, No. 1, 71--92 (1992; Zbl 0807.16027); translation from Algebra Anal. 4, No. 1, 75--97 (1992)
Bavula, V. V. Simple \(D[X,Y;\sigma,a]\)-modules. (English. Russian original) Zbl 0810.16003 Ukr. Math. J. 44, No. 12, 1500-1511 (1992); translation from Ukr. Mat. Zh. 44, No. 12, 1628-1644 (1992). Reviewer: W.M.McGovern (Seattle) MSC: 16D60 16S36 17B35 17B37 16S30 PDFBibTeX XMLCite \textit{V. V. Bavula}, Ukr. Mat. Zh. 44, No. 12, 1628--1644 (1992; Zbl 0810.16003); translation from Ukr. Mat. Zh. 44, No. 12, 1628--1644 (1992) Full Text: DOI
Bavula, Vladimir Generalized Weyl algebras, kernel and tensor-simple algebras, their simple modules. (English) Zbl 0802.17006 Dlab, Vlastimil (ed.) et al., Proceedings of the sixth international conference on representations of algebras, held at the Carleton University, Ottawa, Canada, August 19-22, 1992. Ottawa: Carleton University, Mathematics and Statistics, Carleton-Ottawa Math. Lect. Note Ser. 14, Exp. 5, 23 p. (1992). Reviewer: M.P.Holland (Sheffield) MSC: 17B37 16S32 16D60 PDFBibTeX XMLCite \textit{V. Bavula}, Carleton-Ottawa Math. Lect. Note Ser. 14, Exp. 5, 23 p. (1992; Zbl 0802.17006)