Alpha Skew J-McCoy Rings

Subject Areas : Statistics

M. Vahdani Mehrabadi ¹ (Department of Mathematics, Islamic Azad University, Central Tehran Branch, 13185/768,)
Sh. sahebi ² (Department of Mathematics, Islamic Azad University, Central Tehran Branch, 13185/768,)

Received: 2017-09-14 Accepted : 2019-06-23 Published : 1970-01-01

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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