Volume 7, Issue 3 (Vol.7, No.3, 2021)                   mmr 2021, 7(3): 585-590 | Back to browse issues page


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sahebi S. Semi-Armendariz and Semi-McCoy rings. mmr 2021; 7 (3) :585-590
URL: http://mmr.khu.ac.ir/article-1-2915-en.html
, sahebi@iauctb.ac.ir
Abstract:   (665 Views)
We introduce the notion of Semi-Armendariz (resp. Semi-McCoy) rings, which are a subclass of J-Armendariz (resp. J-McCoy rings) and investigate their properties. A ring R is called Semi-Armendariz (Semi-McCoy) if  is Armendariz (McCoy). As special case, we show that the class of Semi-Armendariz (resp. Semi-McCoy) rings lies properly between the class of one-sided quasi-duo rings and the class of J-Armendariz (resp. J-McCoy) rings. We show that a ring R is Semi-Armendariz (resp. Semi-McCoy) iff R[[x]] is Semi-Armendariz (resp. Semi-McCoy) iff for any idempotent , eRe is Semi-Armendariz (resp. Semi-McCoy) iff the n-by-n upper triangular matrix ring Tn(R)  is Semi-Armendariz (resp. Semi-McCoy). But, by an example we show that for a ring R and n>1,  is not necessarily Semi-Armendariz (Semi-McCoy) and so R is not Morita invariant. At last, we prove that for an automorphism  a ring R is Semi-Armendariz (resp. Semi-McCoy) iff the Jordan structure of R ( is Semi-Armendariz (resp. Semi-McCoy) and so we identify the Jacobson radical of A.
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Type of Study: S | Subject: alg
Received: 2019/02/19 | Revised: 2022/05/7 | Accepted: 2020/03/1 | Published: 2021/12/1 | ePublished: 2021/12/1

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