Results 1 to 10 of about 42 (33)
AxiomsThe explicit forms of idempotent and semicentral idempotent triangular matrices over an additively idempotent semiring are obtained. We define a diamond composition of idempotents and give a representation of an idempotent n×n matrix as an (n−1)th degree
Dimitrinka Vladeva
exaly +4 more sources
Amitsur's theorem, semicentral idempotents, and additively idempotent semirings
Open MathematicsThe article explores research findings akin to Amitsur’s theorem, asserting that any derivation within a matrix ring can be expressed as the sum of an inner derivation and a hereditary derivation.
Rachev Martin, Trendafilov Ivan
exaly +3 more sources
On Semiabelian π-Regular Rings
International Journal of Mathematics and Mathematical Sciences, 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
doaj +2 more sources
SEMICENTRAL IDEMPOTENTS IN A RING [PDF]
Journal of the Korean Mathematical Society, 2014 Let R be a ring with identity 1, I(R) be the set of all nonunit idempotents in R and Sl(R) (resp. Sr(R)) be the set of all left (resp. right) semicentral idempotents in R. In this paper, the following are investigated: (1) e ∈ Sl(R) (resp. e ∈ Sr(R)) if and only if re = ere (resp.
Juncheol Han, Yang Lee
exaly +2 more sources
A note on semicentral idempotents [PDF]
Communications in Algebra, 2016 In this note we answer the question raised by Han et al. in J. Korean Math. Soc (2014) whether an idempotent isomorphic to a semicentral idempotent is itself semicentral. We show that rings with this property are precisely the Dedekind-finite rings. An application to module theory is given.
Lomp, Christian, Matczuk, Jerzy
openaire +2 more sources
A CHARACTERIZATION OF BAER-IDEALS [PDF]
Journal of Algebraic Systems, 2014 An ideal I of a ring R is called right Baer-ideal if there exists an idempotent e 2 R such that r(I) = eR. We know that R is quasi-Baer if every ideal of R is a right Baer-ideal, R is n-generalized right quasi-Baer if for each I E R the ideal In is right
Ali Taherifar
doaj +1 more source
A SUBCLASS OF BAER IDEALS AND ITS APPLICATIONS [PDF]
Journal of Algebraic SystemsAn ideal $I$ of a ring $R$ is called a right strongly Baer ideal if $r(I)=r(e)$, where $e$ is an idempotent, and there are right semicentral idempotents $e_{i}$ ($1\leq i\leq n$) with $ReR=Re_{1}R\cap Re_{2}R\cap...\cap Re_{n}R$ and each ideal $Re_{i}R ...
Zainab Gharabagi, Ali Taherifar
doaj +1 more source
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