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SOME EXAMPLES OF QUASI-ARMENDARIZ RINGS

  • Hashemi, Ebrahim
  • Published : 2007.08.31

Abstract

In [12], McCoy proved that if R is a commutative ring, then whenever g(x) is a zero-divisor in R[x], there exists a nonzero c $\in$ R such that cg(x) = 0. In this paper, first we extend this result to monoid rings. Then for a monoid M, we give some examples of M-quasi-Armendariz rings which are a generalization of quasi-Armendariz rings. Every reduced ring is M-quasi-Armendariz for any unique product monoid M and any strictly totally ordered monoid $(M,\;{\leq})$. Also $T_4(R)$ is M-quasi-Armendariz when R is reduced and M-Armendariz.

Keywords

Armendariz rings;quasi-Armendariz rings;monoid rings;unique product monoid rings

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