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مجلة التربية والعلم, 2006 The main goal of work is to introduce and study a new type of regular rings called - regular rings. That is, a ring R is said to be - regular if for every aR there exists bR and a positive integer n≠1 such that a=abna.
SANHAN M. SALIH, ABDUL AALI J. MOHAMMAD
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On Semiabelian π-Regular Rings [PDF]
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
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الحلقات التی فیها کل مقاس بسیط ایمن مسطح
Al-Rafidain Journal of Computer Sciences and Mathematics, 2004 Abstract. A ring R is called a left (right) SF-ring if simple left (right) R-modules areflat. It is still unknown whether a left (right) SF-ring is von Neumann regular. In thispaper, we give some conditions for a left (right) SF-ring to be (a) von Neumann regular;(b) strongly regular; (c) division ring.
Raida D. Mahmood
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Von Neumann Regular McCoy Rings [PDF]
Journal of Sciences, Islamic Republic of Iran, 2021 A ring R is said to be right McCoy, if for every f(x),g(x) in the polynomial ring R[x], with f(x)g(x)=0 there exists a nonzero element cϵR with f(x)c=0. In this note, we show that von Neumann regular McCoy rings are abelian. This gives a positive
Masoome Zahiri
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GENERALIZATION OF VON-NEUMANN REGULAR RINGS TO VON-NEUMANN REGULAR MODULES
Barekeng, 2023 An element r in a commutative ring R is called regular if there exist s∈R such that rsr=r. Ring R is called vN (von-Neumann)-regular ring if every element is regular. Recall that for any ring R always can be considered as module over itself.
Hubbi Muhammad, Sri Wahyuni
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On Strongly – Regular Rings [PDF]
مجلة التربية والعلم, 2009 The main goal of the work is to study a strongly -regular rings, which was introduce by Mohammad A. J. and Salih. S. M. in (2006). That is, a ring R is said to be strongly -regular if for every a R there exists bR and a positive integer n≠1 such ...
Baida S. Abdullah
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Al-Rafidain Journal of Computer Sciences and Mathematics, 2011 As a generalization of regular rings, that is a ring is called n-regular if for all . In this paper, we first give various properties of n-regular rings.
Raida Mahmood, Mohammed Youns
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Imbedding a Regular Ring in a Regular Ring with Identity [PDF]
Nagoya Mathematical Journal, 1966 In [1] L. Fuchs and I. Halperin have proved that a regular ring R is isomorphic to a two-sided ideal of a regular ring with identity. ([1] Theorem 1). Their methed is to imbed the regular ring R in the ring of all pairs (a, p) with a ∊ R and p from a suitable commutative regular ring S with identity such that R is an algebra over S.
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Varieties of ∗-regular rings [PDF]
Mathematica Slovaca, 2020 Abstract Given a subdirectly irreducible ∗-regular ring R, we show that R is a homomorphic image of a regular ∗-subring of an ultraproduct of the (simple) eRe, e in the minimal ideal of R; moreover, R (with unit) is directly finite if all eRe are unit-regular.
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Science Journal of University of Zakho, 2017 In this paper we introduce the concept of -clean ring and we discuss some relations between - clean ring and other rings with explaining by some examples. Also, we give some basic properties of it.
Shaimaa S. Esa, Hewa S. Faris
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