Quasi-Armendariz rings relative to a monoid |
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Authors: | Ebrahim Hashemi |
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Institution: | Department of Mathematics, Shahrood University of Technology, P.O. Box 316-3619995161, Shahrood, Iran |
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Abstract: | For a monoid M, we introduce M-quasi-Armendariz rings which are a generalization of quasi-Armendariz rings, and investigate their properties. The M-quasi-Armendariz condition is a Morita invariant property. The class of M-quasi-Armendariz rings is closed under some kinds of upper triangular matrix rings. Every semiprime ring is M-quasi-Armendariz for any unique product monoid and any strictly totally ordered monoid M. Moreover, we study the relationship between the quasi-Baer property of a ring R and those of the monoid ring RM]. Every quasi-Baer ring is M-quasi-Armendariz for any unique product monoid and any strictly totally ordered monoid M. |
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Keywords: | 16S36 16N60 16P60 |
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