Multiplicative Maps on Generalized n-matrix Rings

2022/05/30 by Ferreira, Bruno L. M., Jabeen, Aisha
#16W99 #47B47 #47L35 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2205.15728

Abstract

Let \mathfrakR and \mathfrakR' be two associative rings (not necessarily with the identity elements). A bijective map φ of \mathfrakR onto \mathfrakR' is called a m-multiplicative isomorphism if φ(x₁ ⋯ x_m) = φ(x₁) ⋯ φ(x_m) for all x₁, ⋯ ,x_m∈ \mathfrakR. In this article, we establish a condition on generalized n-matrix rings, that assures that multiplicative maps are additive on generalized n-matrix rings under certain restrictions. And then, we apply our result for study of m-multiplicative isomorphism and m-multiplicative derivation on generalized n-matrix rings.

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