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

Aisha Jabeen; Bruno L. M. Ferreira

doi:10.56754/0719-0646.2601.033

Authors

Aisha Jabeen Department of Physics, Jamia Millia Islamia, New Delhi-110025, India. https://orcid.org/0000-0002-8144-322X
Bruno L. M. Ferreira Federal University of Technology-Paraná-Brazil, Av. Professora Laura Pacheco Bastos, 800, 85053-510, Guarapuava, Brazil – Federal University of ABC, Av. dos Estados, 5001, 09210-580, Santo André - SP-Brazil - São Paulo University, Rua Matão, 1010, CEP 05508-090, São Paulo, Brazil. https://orcid.org/0000-0003-1621-8197

DOI:

https://doi.org/10.56754/0719-0646.2601.033

Keywords:

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

Abstract

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.

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