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On the binary system of factors of formal matrix rings. (English) Zbl 07250683
Summary: We investigate the formal matrix ring over $$R$$ defined by a certain system of factors. We give a method for constructing formal matrix rings from non-negative integer matrices. We also show that the principal factor matrix of a binary system of factors determine the structure of the system.
MSC:
 16S50 Endomorphism rings; matrix rings 15B99 Special matrices
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References:
 [1] Abyzov, A. N.; Tapkin, D. T., Formal matrix rings and their isomorphisms, Sib. Math. J. 56 (2015), 955-967 translated from Sib. Mat. Zh. 56 2015 1199-1214 [2] Abyzov, A. N.; Tapkin, D. T., On certain classes of rings of formal matrices, Russ. Math. 59 (2015), 1-12 translated from Izv. Vyssh. Uchebn. Zaved., Mat. 2015 2015 3-14 [3] Auslander, M.; Reiten, I.; Smalø, S. O., Representation Theory of Artin Algebras, Cambridge Studies in Advanced Mathematics 36. Cambridge University Press, Cambridge (1995) [4] Varadarajan, A. Haghany K., Study of formal triangular matrix rings, Commun. Algebra 27 (1999), 5507-5525 [5] Varadarajan, A. Haghany K., Study of modules over formal triangular matrix rings, J. Pure Appl. Algebra 147 (2000), 41-58 [6] Krylov, P. A., Isomorphism of generalized matrix rings, Algebra Logic 47 (2008), 258-262 translated from Algebra Logika 47 2008 456-463 [7] Krylov, P. A., Injective modules over formal matrix rings, Sib. Math. J. 51 (2010), 72-77 translated from Sib. Mat. Zh. 51 2010 90-97 [8] Krylov, P. A.; Tuganbaev, A. A., Modules over formal matrix rings, J. Math. Sci., New York 171 (2010), 248-295 translated from Fundam. Prikl. Mat. 15 2009 145-211 [9] Krylov, P. A.; Tuganbaev, A. A., Formal matrices and their determinants, J. Math. Sci., New York 211 (2015), 341-380 translated from Fundam. Prikl. Mat. 19 2014 65-119 [10] Lam, T. Y., Lectures on Modules and Rings, Graduate Texts in Mathematics 189. Springer, New York (1999) [11] Morita, K., Duality for modules and its applications to the theory of rings with minimum conditions, Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A 6 (1958), 83-142 [12] Müller, M., Rings of quotients of generalized matrix rings, Commun. Algebra 15 (1987), 1991-2015 [13] Nicholson, W. K.; Watters, J. F., Classes of simple modules and triangular rings, Commun. Algebra 20 (1992), 141-153 [14] Tang, G.; Li, C.; Zhou, Y., Study of Morita contexts, Commun. Algebra 42 (2014), 1668-1681 [15] Tang, G.; Zhou, Y., Strong cleanness of generalized matrix rings over a local ring, Linear Algebra Appl. 437 (2012), 2546-2559 [16] Tang, G.; Zhou, Y., A class of formal matrix rings, Linear Algebra Appl. 438 (2013), 4672-4688
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