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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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A Generalization of Von Neumann Regular Rings [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2009 In this paper, we introduce a new ring which is a generalization of Von Neumann regular rings and we call it a centrally regular ring. Several properties of this ring are proved and we have extended many properties of regular rings to centrally regular ...
Adil Jabbar
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Some Properties of Strongly Principally Self-Injective Modules [PDF]
Journal of Applied Sciences and Nanotechnology, 2022 The idea of generalizing quasi injective by employing a new term is introduced in this paper. The introduction of principally self-injective modules, which are principally self-injective modules.
Khalid Munshid +2 more
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On Rings Whose Simple Singular R-Modules Are Flat, I [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2010 In this paper we investigate von Neumann regularity of rings whose simple singular right R-modules are flat. It is proved that a ring R is strongly regular if and only if R is a semiprime right quasi-duo ring whose simple singular right R-modules are ...
Raida Mahmood, Abdullah Abdul-Jabbar
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Stable range conditions for abelian and duo rings
Математичні Студії, 2022 The article deals with the following question: when does the classical ring of quotients of a duo ring exist and idempotents in the classical ring of quotients $Q_{Cl} (R)$ are there idempotents in $R$?
A. A. Dmytruk +2 more
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Al-Rafidain Journal of Computer Sciences and Mathematics, 2014 A ring R is called local ring if it has exactly one maximal ideal. In this paper, we introduce some characterization and basic properties of this ring. Also, we studied the relation between local rings and Von Neumann regular rings and strongly regular ...
Zubayda Ibraheem, Anees Fthee
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Tikrit Journal of Pure Science, 2020 Let R be a commutative ring, the Pseudo – Von Neumann regular graph of the ring R is define as a graph whose vertex set consists of all elements of R and any two distinct vertices a and b are adjacent if and only if , this graph is denoted by P-VG(R ...
Nermen J. Khalel, Nabeel E. Arif
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On Regularity and Flatness [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2004 A ring R is called a right SF-ring if all its simple right R-modules are flat. It is well known that Von Neumann regular rings are right and left SF-rings. In this paper we study conditions under which SF-rings are strongly regular.
Nazar Shuker
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On Von Neumann Regular Rings [PDF]
Canadian Mathematical Bulletin, 1974 Recently, in the Research Problems of Canadian Mathematical Bulletin, Vol. 14, No. 4, 1971, there appeared a problem which asks “Is a prime Von Neumann regular ring pimitive?” While we are not able to settle this question one way or the other, we prove that in a Von Neumann regular ring, there is a maximal annihilator right ideal if and only if there ...
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