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@article{FPM_2014_19_1_a5,
author = {P. A. Krylov and A. A. Tuganbaev},
title = {Formal matrices and their determinants},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {65--119},
publisher = {mathdoc},
volume = {19},
number = {1},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2014_19_1_a5/}
}
P. A. Krylov; A. A. Tuganbaev. Formal matrices and their determinants. Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 1, pp. 65-119. http://geodesic.mathdoc.fr/item/FPM_2014_19_1_a5/
[1] Abyzov A. N., Tapkin D. T., “O nekotorykh klassakh kolets formalnykh matrits”, Izv. vyssh. uchebn. zaved. Matematika (to appear)
[2] Krylov P. A., “Ob izomorfizme kolets obobschënnykh matrits”, Algebra i logika, 47:4 (2008), 456–463 | MR | Zbl
[3] Krylov P. A., “O gruppe $K_0$ koltsa obobschënnykh matrits”, Algebra i logika, 52:3 (2013), 370–385 | MR | Zbl
[4] Krylov P. A., “Vychislenie gruppy $K_1$ koltsa obobschënnykh matrits”, Sib. mat. zhurn., 55:4 (2014), 783–789
[5] Tuganbaev A., Teoriya kolets. Arifmeticheskie moduli i koltsa, MTsNMO, M., 2009
[6] Baba Y., Oshiro K., Classical Artinian Rings and Related Topics, World Scientific, London, 2009 | MR
[7] Climent J.-J., Navarro P. R., Tortosa L., “On the arithmetic of the endomorphism ring $\mathrm{End}(\mathbb Z_p\times\mathbb Z_{p^2})$”, Appl. Algebra Eng. Comm. Comput., 22:2 (2011), 91–108 | DOI | MR | Zbl
[8] Cohen M., “Morita context related to finite automorphism groups of rings”, Pacific J. Math., 98 (1982), 37–54 | DOI | MR | Zbl
[9] Fossum R. M., Griffith P. A., Reiten I., “Trivial extensions of Abelian categories”, Homological Algebra of Trivial Extensions of Abelian Catergories with Applications to Ring Theory, Lect. Notes Math., 456, Springer, Berlin, 1975, 1–122 | DOI | MR
[10] Gurgun O., Halicioglu S., Harmanci A., Quasipolarity of generalized matrix rings, 2013, arXiv: 1303.3173[math.RA]
[11] Gurgun O., Halicioglu S., Harmanci A., Strong $J$-cleanness of formal matrix rings, 2013, arXiv: 1308.4105v1[math.RA]
[12] Horn R. A., Johnson Ch. R., Matrix Analysis, Cambridge Univ. Press, Cambridge, 2012
[13] Huang Q., Tang G., “Quasipolar property of trivial Morita context”, Int. J. Pure Appl. Math., 90:4 (2014), 423–431 | DOI | Zbl
[14] Huang Q., Tang G., Zhou Y., “Quasipolar property of generalized matrix rings”, Commun. Algebra, 42:9 (2014), 3883–3894 | DOI | MR | Zbl
[15] Kim K. H., Boolean Matrix Theory and Applications, Marcel Dekker, New York, 1982 | MR | Zbl
[16] Krylov P. A., “Determinants of generalized matrises of order 2”, J. Math. Sci. (to appear)
[17] Krylov P. A., Mikhalev A. V., Tuganbaev A. A., Endomorphism Rings of Abelian Groups, Kluwer Academic, Dordrecht, 2003 | MR | Zbl
[18] Krylov P. A., Tuganbaev A. A., Modules over Discrete Valuation Domains, De Gruyter Exp. Math., 43, Walter de Gruyter, Berlin, 2008 | DOI | Zbl
[19] Krylov P. A., Tuganbaev A. A., “Modules over formal matrix rings”, J. Math. Sci., 171:2 (2010), 248–295 | DOI | MR | Zbl
[20] Palmer I., “The global homological dimension of semi-trivial extensions of rings”, Math. Scand., 37 (1975), 223–256 | MR
[21] Sands A. D., “Radicals and Morita contexts”, J. Algebra, 24 (1973), 335–345 | DOI | MR | Zbl
[22] Tang G., Li Ch., Zhou Y., “Study of Morita contexts”, Commun. Algebra, 42 (2014), 1668–1681 | DOI | MR | Zbl
[23] Tang G., Zhou Y., “Strong cleanness of generalized matrix rings over a local ring”, Linear Algebra Appl., 437 (2012), 2546–2559 | DOI | MR | Zbl
[24] Tang G., Zhou Y., “A class of formal matrix rings”, Linear Algebra Appl., 438:12 (2013), 4672–4688 | DOI | MR | Zbl
[25] Tuganbaev A., Semidistributive Modules and Rings, Kluwer Academic, Dordrecht, 1998 | MR | Zbl