Multiplicative maps on generalized \(n\)-matrix rings




Let \(\mathfrak{R}\) and \(\mathfrak{R}'\) be two associative rings (not necessarily with identity elements). A bijective map \(\varphi\) of \(\mathfrak{R}\) onto \(\mathfrak{R}'\) is called an \textit{\(m\)-multiplicative isomorphism} if {\(\varphi (x_{1} \cdots x_{m}) = \varphi(x_{1}) \cdots \varphi(x_{m})\)} for all \(x_{1}, \dotsc ,x_{m}\in \mathfrak{R}.\) In this article, we establish a condition on generalized matrix rings, that assures that multiplicative maps are additive. And then, we apply our result for study of \(m\)-multiplicative isomorphisms and \(m\)-multiplicative derivations on generalized matrix rings.


m-multiplicative maps , m-multiplicative derivations , generalized n-matrix rings , additivity

Mathematics Subject Classification:

16W99 , 47B47 , 47L35
  • Pages: 33–51
  • Date Published: 2024-03-25
  • Vol. 26 No. 1 (2024)

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How to Cite

A. Jabeen and B. L. M. Ferreira, “Multiplicative maps on generalized \(n\)-matrix rings”, CUBO, vol. 26, no. 1, pp. 33–51, Mar. 2024.