On realization and isomorphism problems for formal matrix rings
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 219 (2023), pp. 39-43.

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We consider realization and isomorphism problems for formal matrix rings over a given ring. Principal multiplier matrices of such rings play an important role in this case.
Keywords: formal matrix ring
Mots-clés : principal multiplier matrix.
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P. A. Krylov; A. Tuganbaev. On realization and isomorphism problems for formal matrix rings. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 219 (2023), pp. 39-43. http://geodesic.mathdoc.fr/item/INTO_2023_219_a2/

[1] Abyzov A. N., Tapkin D. T., “Koltsa formalnykh matrits i ikh izomorfizmy”, Sib. mat. zh., 56:6 (2015), 1199–1214 | DOI | MR

[2] Abyzov A. N., Tapkin D. T., “O nekotorykh klassakh kolets formalnykh matrits”, Izv. vuzov. Mat., 2015, no. 3, 3–14

[3] Krylov P. A., “Ob izomorfizme kolets obobschennykh matrits”, Algebra i logika., 47:4 (2008), 456–463 | MR | Zbl

[4] Krylov P. A., Norbosambuev Ts. D., “Avtomorfizmy algebr formalnykh matrits”, Sib. mat. zh., 59:5 (2018), 1116–1127 | DOI

[5] Krylov P. A., Tuganbaev A. A., “Gruppy avtomorfizmov kolets formalnykh matrits”, Itogi nauki tekhn. Sovr. mat. prilozh. Temat. obz., 164 (2019), 96–124 | MR

[6] Tapkin D. T., “Koltsa formalnykh matrits i obobschenie algebry intsidentnosti”, Chebyshev. sb., 16:3 (2015), 442–449

[7] Tapkin D. T., “Izomorfizmy kolets intsidentnosti formalnykh matrits”, Izv. vuzov. Mat., 2017, no. 12, 84–91

[8] Auslander M., Reiten I., Smalø S. O., Representation Theory of Artin Algebras, Cambridge Univ. Press, Cambridge, 1995

[9] Baba Y., Oshiro K., Classical Artinian Rings and Related Topics, World Scientific, New Jersey–London–Singapore, 2009

[10] Chen W., Deng G., Su H., “On the binary system of factors of formal matrix rings”, Czech. Math. J., 70 (2020), 693–709

[11] Krylov P. A., Tuganbaev A. A., Formal Matrices, Springer-Verlag, Berlin, 2017

[12] Krylov P. A., Tuganbaev A. A., Automorphisms of formal matrix rings, arXiv: arXiv:2204.13332 [math.RA]

[13] Tang G., Zhou Y., “A class of formal matrix rings”, Lin. Algebra Appl., 438:12 (2013), 4672–4688