On Semiprime Right Goldie Mccoy Rings
نویسنده
چکیده
In this note we first show that for a right (resp. left) Ore ring R and an automorphism σ of R, if R is σ-skew McCoy then the classical right (resp. left) quotient ring Q(R) of R is σ̄-skew McCoy. This gives a positive answer to the question posed in Başer et al. [1]. We also characterize semiprime right Goldie (von Neumann regular) McCoy (σ-skew McCoy) rings.
منابع مشابه
Goldie Ranks of Skew Power Series Rings of Automorphic Type
Let A be a semprime, right noetherian ring equipped with an automorphism α, and let B := A[[y;α]] denote the corresponding skew power series ring (which is also semiprime and right noetherian). We prove that the Goldie ranks of A and B are equal. We also record applications to induced ideals.
متن کاملGoldie Conditions for Ore Extensions over Semiprime Rings
Let R be a ring, σ an injective endomorphism of R and δ a σderivation of R. We prove that if R is semiprime left Goldie then the same holds for the Ore extension R[x;σ, δ] and both rings have the same left uniform dimension.
متن کاملOn annihilator ideals in skew polynomial rings
This article examines annihilators in the skew polynomial ring $R[x;alpha,delta]$. A ring is strongly right $AB$ if everynon-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property ($A$) and the conditions asked by P.P. Nielsen. We assume that $R$ is an ($alpha$,$delta$)-compatible ring, and prove that, if $R$ is ni...
متن کاملThe largest strong left quotient ring of a ring
For an arbitrary ring R, the largest strong left quotient ring Ql (R) of R and the strong left localization radical lR are introduced and their properties are studied in detail. In particular, it is proved that Ql (Q s l (R)) ≃ Q s l (R), l s R/ls R = 0 and a criterion is given for the ring Ql (R) to be a semisimple ring. There is a canonical homomorphism from the classical left quotient ring Q...
متن کاملOn semiperfect rings of injective dimension one
We give a characterization of right Noetherian semiprime semiperfect and semidistributive rings with inj. dimAAA 6 1.
متن کامل