Geodesic
Automorphism groups of formal matrix rings
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 164 (2019), pp. 96-124.

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We study automorphism groups of formal matrix algebras. In some cases, such a group turns out the semidirect product of subgroups with familiar structure.
Keywords: split extension of an ideal
Mots-clés : automorphism, formal matrix algebra. 
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P. A. Krylov; A. A. Tuganbaev. Automorphism groups of formal matrix rings. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 164 (2019), pp. 96-124. http://geodesic.mathdoc.fr/item/INTO_2019_164_a2/

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

[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., Norbosambuev Ts. D., “Avtomorfizmy algebr formalnykh matrits”, Sib. mat. zh., 59:5 (2018), 1116–1127 | Zbl

[4] Krylov P. A., Norbosambuev Ts. D., “Gruppa avtomorfizmov odnogo klassa algebr formalnykh matrits”, Vestn. Tomsk. gos. un-ta. Mat. Mekh., 53:3 (2018), 16–21

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

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

[7] Ánh P. N., van Wyk L., “Automorphism groups of generalized triangular matrix rings”, Lin. Alg. Appl., 434 (2011), 1018–1026 | DOI | MR | Zbl

[8] Ánh P. N., van Wyk L., “Isomorphisms between strongly triangular matrix rings”, Lin. Alg. Appl., 438 (2013), 4374–4381 | DOI | MR | Zbl

[9] Barker J. P., “Automorphism groups of algebras of triangular matrices”, Lin. Alg. Appl., 121 (1989), 207–215 | DOI | MR | Zbl

[10] Birkenmeier G. F., Heatherly H. E., Kim J. Y., Park J. K., “Triangular matrix representations”, J. Algebra., 230 (2000), 558–595 | DOI | MR | Zbl

[11] Boboc C., Dǎscǎlescu S., van Wyk L., “Isomorphisms between Morita context rings”, Lin. Multilin. Algebra., 60:5 (2012), 545–563 | DOI | MR | Zbl

[12] Chekhlov A., Danchev P., “$n$-Hopfian and $n$-co-Hopfian Abelian groups”, Hacet. J. Math. Stat., 48:2 (2019), 479–489 | MR

[13] Faith C., Algebra: Rings, Modules and Categories, Springer-Verlag, Berlin, 1973 | MR | Zbl

[14] Isaacs I. M., “Automorphisms of matrix algebras over commutative rings”, Lin. Alg. Appl., 31 (1980), 215–231 | DOI | MR | Zbl

[15] Jøndrup S., “The group of automorphisms of certain subalgebras of matrix algebras”, J. Algebra., 141 (1991), 106–114 | DOI | MR

[16] Jøndrup S., “Automorphisms and derivations of upper triangular matrix rings”, Lin. Alg. Appl., 221 (1995), 205–218 | DOI | MR

[17] Kaigorodov E. V., Krylov P. A., “On some classes of Hopfian Abelian groups and modules”, J. Math. Sci., 230:3, 392–397 | DOI | MR | Zbl

[18] Kezlan T. P., “A note on algebra automorphisms of triangular matrices over commutative rings”, Lin. Alg. Appl., 135, 181–184 | DOI | MR | Zbl

[19] Khazal R., Dǎscǎlescu S., van Wyk L., “Isomorphisms of generalized triangular matrix rings and recovery of tiles”, Int. J. Math. Math. Sci., 2003:9 (2003), 533–538 | DOI | MR | Zbl

[20] Krylov P. A., “Affine module groups and their automorphisms”, Algebra Logic., 40:1 (2001), 34–46 | DOI | MR | Zbl

[21] Krylov P., Tuganbaev A., Formal Matrices, Springer-Verlag, 2017 | MR | Zbl

[22] Li Y.-B., Wei F., “Semi-centralizing maps of generalized matrix algebras”, Lin. Alg. Appl., 436 (2012), 1122–1153 | DOI | MR | Zbl

[23] Pierce R. S., Associative Algebras, Springer-Verlag, Berlin, 1982 | MR | Zbl

[24] Xiao Z., Wei F., “Commuting mappings of generalized matrix algebras”, Lin. Alg. Appl., 433 (2010), 2178–2197 | DOI | MR | Zbl

[25] Xiao Z., Wei F., “Commuting traces and Lie isomorphisms of generalized matrix algebras”, Operators and Matrices., 8 (2014), 821–847 | DOI | MR | Zbl