Jordan homomorphisms of the structural matrix algebras

Abstract

Let C be a commutative ring with identity and let. be quasi- order relation on {1, 2,..., n}. Then Mn ( C,.) will denote the structural matrix algebra over C. In this study, we show that, Theorem 4.1 of Benkovi. c [ Jordan homomorphisms on triangular matrices. Linear and Multilinear Algebra. 2005; 53: 345- 356] and Theorem 7 of Jacobson N. and Rickart C. [ Jordan homomorphisms of rings. Trans. Amer. Math. Soc. 1950; 69: 479- 502] can be extended to two special cases, one for each theorem of structural matrix algebras.