Multiplicative maps on generalized \(n\)-matrix rings
- Aisha Jabeen ajabeen329@gmail.com
- Bruno L. M. Ferreira brunolmfalg@gmail.com
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https://doi.org/10.56754/0719-0646.2601.033Abstract
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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X. Cheng and W. Jing, “Additivity of maps on triangular algebras,” Electron. J. Linear Algebra, vol. 17, pp. 597–615, 2008, doi: 10.13001/1081-3810.1285.
M. N. Daif, “When is a multiplicative derivation additive?” Internat. J. Math. Math. Sci., vol. 14, no. 3, pp. 615–618, 1991, doi: 10.1155/S0161171291000844.
B. L. M. Ferreira, “Multiplicative maps on triangular n-matrix rings,” Internat. J. Math., Game Theory and Algebra, vol. 23, no. 2, pp. 1–14, 2014.
Y. Li and Z. Xiao, “Additivity of maps on generalized matrix algebras,” Electron. J. Linear Algebra, vol. 22, pp. 743–757, 2011, doi: 10.13001/1081-3810.1471.
F. Y. Lu and J. H. Xie, “Multiplicative mappings of rings,” Acta Math. Sin. (Engl. Ser.), vol. 22, no. 4, pp. 1017–1020, 2006, doi: 10.1007/s10114-005-0620-7.
F. Lu, “Multiplicative mappings of operator algebras,” Linear Algebra Appl., vol. 347, pp. 283–291, 2002, doi: 10.1016/S0024-3795(01)00560-2.
W. S. Martindale, III, “When are multiplicative mappings additive?” Proc. Amer. Math. Soc., vol. 21, pp. 695–698, 1969, doi: 10.2307/2036449.
G. Tang and Y. Zhou, “A class of formal matrix rings,” Linear Algebra Appl., vol. 438, no. 12, pp. 4672–4688, 2013, doi: 10.1016/j.laa.2013.02.019.
Y. Wang, “The additivity of multiplicative maps on rings,” Comm. Algebra, vol. 37, no. 7, pp. 2351–2356, 2009, doi: 10.1080/00927870802623369.
Y. Wang, “Additivity of multiplicative maps on triangular rings,” Linear Algebra Appl., vol. 434, no. 3, pp. 625–635, 2011, doi: 10.1016/j.laa.2010.09.015.
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