Let R be an arbitrary ring with identity and M a right R-module with S = EndR(M). In this paper, we introduce a class of modules that is a generalization of principally projective (or simply p.p.) rings and Baer modules. ...

We introduce the notion of central Armendariz rings which are a generalization of Armendariz rings and investigate their properties. We show that the class of central Armendariz rings lies strictly between classes of ...

In this note, we introduce abelian modules as a generalization of abelian rings. Let R be an arbitrary ring with identity. A module M is called abelian if, for any m 2 M and any a 2 R, any idempotent e 2 R, mae = mea. ...

In this note we introduce central linear Armendariz rings as a generalization of Armendariz rings and investigate their properties

[No Abstract Available]

We say a module MR a semicommutative module if for any m 2 M and any a 2 R, ma = 0 implies mRa = 0. This paper gives various properties of reduced, Armendariz, Baer, Quasi-Baer, p:p: and p:q:-Baer rings to extend to ...

Let R be a ring with identity,M a right R-module and S = EndR(M). In this note, we introduce S-semicommutative, S-Baer, S-q.-Baer and S-p.q.-Baer modules. We study the relations between these classes of modules. Also we ...

We investigate some properties of Rickart modules defined by Rizvi and Roman. Let R be an arbitrary ring with identity and M be a right R-module with S = EndR(M). A module M is called to be Rickart if for any f 2 S, ...

Let α be an endomorphism of an arbitrary ring R with identity. In this note, we introduce the notion of α-abelian rings which generalizes abelian rings. We prove that α-reduced rings, α-symmetric rings, α-semicommutative ...

Let R be an arbitrary ring with identity and M a right R-module with S = EndR(M). In this paper, we introduce a class of modules that is a generalization of principally quasi-Baer rings and Baer modules. The mod- ule ...