{"title":"Generalized Module Homomorphisms of Triangular Matrix Rings of Order Three","authors":"Jianmin Xing","volume":68,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1136,"pagesEnd":1140,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/5990","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 = \u0002 T M D 0 U N 0 0 V \u0003.<\/p>\r\n","references":"[1] G. M. Benkart and J. M. Osborn, Derivations and automorphisms of\r\nnon associative matrix algebras, Trans. Amer. Math. Soc. 263 (1981) 411-430.\r\n[2] S. P. Coelho and C. P. Milies, Derivations of upper triangular matrix\r\nrings, Linear Alg. Appl. 187 (1993) 263-267.\r\n[3] G. F. Birkenmeier and J. K. Park, Triangular matrix representations of\r\nring extensions, J. Algebra, 265 (2003) 457-477.\r\n[4] S. Jondrup, Automorphism and derivations of triangular matrices, Linear\r\nAlg. Appl. 22 (1995) 205-215.\r\n[5] S. Jondrup, Automorphism of upper triangular matrix rings, Arch. Math.\r\n49 (1987) 497-502.\r\n[6] Giambruno and I. N. Herstein, Derivations with nilpotent values, Rendicoti,\r\nDel Circolo Mathematico Di palermo Serie II, Tommo XXX, (1981) 199-206.\r\n[7] H. Ghahramant and A.Moussavi , Differential polynomial rings,Bulletin\r\nof the Iranian Mathematical Society Vol. 34 No. 2 (2008), 71-96.\r\n[8] SHI Mei Hua and ZENG Qing yi, Module Category over triangular\r\nmatrix rings of order 3, Journal of Zhenjiang university(Science\r\n,Editor),32(5),(2005)481-484.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 68, 2012"}