Results 201 to 210 of about 51,002 (217)

Weakly Regular Rings

Canadian Mathematical Bulletin, 1973
This paper attempts to generalize a property of regular rings, namely,I2=Ifor every right (left) ideal. Rings with this property are called right (left) weakly regular. A ring which is both left and right weakly regular is called weakly regular. Kovacs in [6] proved that, for commutative rings, weak regularity and regularity are equivalent conditions ...
openaire   +2 more sources

Semiregular, weakly regular, and π-regular rings

Journal of Mathematical Sciences, 2002
This is a survey paper related to regular rings and their generalizations. It introduces many rings and modules, such as: semiregular and regular modules, semiregular and regular rings, semiprime and nonsingular rings, weakly \(\pi\)-regular and weakly regular rings, strongly \(\pi\)-regular and \(\pi\)-regular rings, rings of quotients and Pierce ...
openaire   +2 more sources

Semiregular and Weakly Regular Rings

2002
For a module M, we say that a submodule N of M lies above a direct summand of M if there is a direct decomposition M = P⊕Q such that P⊆N and Q⋂N is a superfluous submodule of Q. In this case, Q⋂N is a superfluous submodule of M and Q⋂N⊆J(M).
openaire   +1 more source

On weakly regular modules over commutative rings

Journal of Algebra and Its Applications
In this paper, we introduce the class of weakly (von Neumann) regular modules and study its algebraic properties. We present some characterization of this class of modules. Finally, we show that a ring [Formula: see text] is perfect if and only if every [Formula: see text]-module is weakly regular.
Dawood Hassanzadeh-Lelekaami, Hajar Roshan-Shekalgourabi   +1 more
openaire   +1 more source

ON WEAKLY REGULAR RINGS AND GENERALIZATIONS OF V-RINGS

2011
In this paper, we have studied weakly regular rings and some generalizations of V-rings via GW-ideals. We have shown that: (1) If R is a left weakly regular ring whose maximal left (right) ideals are GW-ideals, then R is strongly regular; (2) If R is a right weakly regular ring whose maximal essential left ideals are GW-ideals, then R is ELT regular ...
Subedi, Tikaram, Buhphang, A. M.
openaire   +1 more source

NI RINGS WHICH ARE WEAKLY π-REGULAR

2009
In this paper, we prove that if a ring R with identity is NI and satisfies (CZ2), then R is right (left) weakly π-regular if and only if R/N ∗(R) is right (left) weakly π-regular, if and only if every strongly prime ideal of R is maximal.
SELVARAJ, C., PETCHİMUTHU, S.
openaire   +1 more source

Weakly Regular and Self-Injective Leavitt Path Algebras Over Arbitrary Graphs

Algebras and Representation Theory, 2010
Gonzalo Aranda Pino, Kulumani M Rangaswamy, Mercedes Siles Molina   +2 more
exaly  

Weakly-Abel rings and weakly exchange rings

Acta Mathematica Hungarica, 2012
Junchao Wei
exaly  

GENERALIZING $\pi$-REGULAR RINGS

Taiwanese Journal of Mathematics, 2015
Peter V Danchev, Janez Šter
exaly  

A note on weakly clean rings

Acta Mathematica Hungarica, 2011
Angelina Chin
exaly