Generalized Module Homomorphisms of Triangular Matrix Rings of Order Three

Authors: Jianmin Xing

Abstract:

Let T,U and V be rings with identity and M be a unitary (T,U)-bimodule, N be a unitary (U, V )- bimodule, D be a unitary (T, V )-bimodule . We characterize homomorphisms and isomorphisms of the generalized matrix ring Γ =  T M D 0 U N 0 0 V .

Keywords: Generalized module homomorphism, ring homomorphism, isomorphisms, triangular matrix rings.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062072

References:

[1] G. M. Benkart and J. M. Osborn, Derivations and automorphisms of non associative matrix algebras, Trans. Amer. Math. Soc. 263 (1981) 411-430.
[2] S. P. Coelho and C. P. Milies, Derivations of upper triangular matrix rings, Linear Alg. Appl. 187 (1993) 263-267.
[3] G. F. Birkenmeier and J. K. Park, Triangular matrix representations of ring extensions, J. Algebra, 265 (2003) 457-477.
[4] S. Jondrup, Automorphism and derivations of triangular matrices, Linear Alg. Appl. 22 (1995) 205-215.
[5] S. Jondrup, Automorphism of upper triangular matrix rings, Arch. Math. 49 (1987) 497-502.
[6] Giambruno and I. N. Herstein, Derivations with nilpotent values, Rendicoti, Del Circolo Mathematico Di palermo Serie II, Tommo XXX, (1981) 199-206.
[7] H. Ghahramant and A.Moussavi , Differential polynomial rings,Bulletin of the Iranian Mathematical Society Vol. 34 No. 2 (2008), 71-96.
[8] SHI Mei Hua and ZENG Qing yi, Module Category over triangular matrix rings of order 3, Journal of Zhenjiang university(Science ,Editor),32(5),(2005)481-484.