Results 11 to 20 of about 93 (57)
On Semiabelian π-Regular Rings [PDF]
International Journal of Mathematics and Mathematical Sciences, Volume 2007, Issue 1, 2007., 2007 A ring R is defined to be semiabelian if every idempotent of R is either right semicentral or left semicentral. It is proved that the set N(R) of nilpotent elements in a π-regular ring R is an ideal of R if and only if R/J(R) is abelian, where J(R) is ...
Weixing Chen
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International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 8, Page 459-466, 2002., 2002 Let R be a ring. The circle operation is the operation a∘b = a + b − ab, for all a, b ∈ R. This operation gives rise to a semigroup called the adjoint semigroup or circle semigroup of R. We investigate rings in which the adjoint semigroup is regular. Examples are given which illustrate and delimit the theory developed.
Henry E. Heatherly, Ralph P. Tucci
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Journal of Applied Mathematics, Volume 2013, Issue 1, 2013., 2013 As a generalization of α‐skew McCoy rings, we introduce the concept of α‐skew π‐McCoy rings, and we study the relationships with another two new generalizations, α‐skew π1‐McCoy rings and α‐skew π2‐McCoy rings, observing the relations with α‐skew McCoy rings, π‐McCoy rings, α‐skew Armendariz rings, π‐regular rings, and other kinds of rings.
Areej M. Abduldaim +2 more
wiley +1 more source
The Generalization of Prime Modules
Algebra, Volume 2013, Issue 1, 2013., 2013 Piecewise prime (PWP) module MR is defined in terms of a set of triangulating idempotents in R. The class of PWP modules properly contains the class of prime modules. Some properties of these modules are investigated here.
M. Gurabi, Masoud Hajarian
wiley +1 more source
Some Notes on Semiabelian Rings
International Journal of Mathematics and Mathematical Sciences, Volume 2011, Issue 1, 2011., 2011 It is proved that if a ring R is semiabelian, then so is the skew polynomial ring R[x; σ], where σ is an endomorphism of R satisfying σ(e) = e for all e ∈ E(R). Some characterizations and properties of semiabelian rings are studied.
Junchao Wei, Nanjie Li, Frank Sommen
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2011, Issue 1, 2011., 2011 We introduce in this paper the concept of left WMC2 rings and concern ourselves with rings containing an injective maximal left ideal. Some known results for left idempotent reflexive rings and left HI rings can be extended to left WMC2 rings. As applications, we are able to give some new characterizations of regular left self‐injective rings with ...
Junchao Wei, Frank Werner
wiley +1 more source
New generalizations of lifting modules [PDF]
, 2016 In this paper, we call a module $M$ almost $\mathcal{I}$-lifting if, for any element $\phi\in S=End_R(M)$, there exists a decomposition $r_M\ell_S(\phi)=A\oplus B$ such that $A\subseteq \phi M$ and $\phi M\cap B\ll M$.
Amouzegar, T.
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Strongly Rickart Modules [PDF]
, 2014 In this paper we introduce and study the concept of strongly Rickart modules and strongly CS-Rickart modules as a stronger than of Rickart modules [8] and CS-Rickart modules[3] respectively.
Al-Saadi, Saad Abdulkadhim +1 more
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Rings having normality in terms of the Jacobson radical [PDF]
, 2020 A ring R is defined to be J-normal if for any a, r∈ R and idempotent e∈ R, ae= 0 implies Rera⊆ J(R) , where J(R) is the Jacobson radical of R. The class of J-normal rings lies between the classes of weakly normal rings and left min-abel rings.
Harmancı, A. +3 more
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International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 We investigate the question whether the p.q.‐Baer center of a ring R can be extended to R. We give several counterexamples to this question and consider some conditions under which the answer may be affirmative. The concept of a generalized p.q.‐Baer property which is a generalization of Baer property of a ring is also introduced.
Tai Keun Kwak
wiley +1 more source