Alpha Skew J-McCoy Rings
Subject Areas : StatisticsM. Vahdani Mehrabadi 1 , Sh. sahebi 2
1 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, 13185/768,
2 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, 13185/768,
Keywords: حلقه چند جمله ای, حلقه مک کوی, حلقه J-مک کوی, حلقه مک کوی ضعیف,
Abstract :
In the present note, for a ring endomorphism Alpha, we introduce Alpha-skew J-McCoy rings, which are a generalization of Alpha-skew McCoy and J-McCoy rings rings and investigate their properties. For a ring R, we show that if Alpha(e)=e for each idempotent e and R Alpha-skew J-McCoy then eRe is Alpha-skew J-McCoy. The converse holds if R is an abelian ring. Also, we prove that if Alphat =idR for some positive integer t and R[x] is Alpha-skew J-McCoy, then R is Alpha-skew J-McCoy. The converse holds if J(R)[x] subset of J(R[x]). Moreover, we give an example to show that the Alpha-skew J-McCoy property does not pass Mn(R). But, for any n, Tn(R) is a Alpha-skew J-McCoy ring if R is a Alpha-skew J-McCoy ring. Also, we prove that If R is right (left) quasi-duo ring and Alpha be an endomorphism of a ring R, then R is Alpha-skew J-McCoy, the converse does not hold in general.
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