WebJul 21, 2009 · semiperfect ring. if idempotents lift modulo J(R)and. R/ J(R) is artinian. The following result clarifies the relationship between semiperfect rings and clean rings; it is Theorem 9 of [2]. This theorem will play a pivotal role in our investigations. Theorem 1.1. The ring R is semiperfect if and only if it is clean and contains no infinite WebIn this article, we investigate when every simple module has a projective (pre)envelope. It is proven that (1) every simple right R-module has a projective preenvelope if and only if the left annihilator of every maximal right ideal of R is finitely generated; (2) every simple right R-module has an epic projective envelope if and only if R is a right PS ring; (3) Every simple …
[2201.03488] Topologically semiperfect topological rings - arXiv.org
WebIn fact, every commutative semiperfect ring is a basic ring and isomorphic to a finite product of local rings, but I do not how to prove it. abstract-algebra; commutative-algebra; Share. Cite. Follow edited Sep 27, 2015 at 7:22. user26857. 1. asked Nov 2, 2012 at 12:20. Aimin Xu Aimin Xu. WebJan 10, 2024 · Abstract: We define topologically semiperfect (complete, separated, right linear) topological rings and characterize them by equivalent conditions. We show that … olly\\u0027s box
Local I-Semipotent Rings - ResearchGate
WebDec 1, 1998 · J. E. Bjork, Rings satisfying the minimal condition on principal left ideals, J. Reine Angew. 236 (1969), 112–119. MathSciNet Google Scholar. J. E. Bjork, Conditions … Definitions The following equivalent definitions of a left perfect ring R are found in Aderson and Fuller: Every left R module has a projective cover.R/J(R) is semisimple and J(R) is left T-nilpotent (that is, for every infinite sequence of elements of J(R) there is an n such that the product of first n terms are zero), … See more In the area of abstract algebra known as ring theory, a left perfect ring is a type of ring in which all left modules have projective covers. The right case is defined by analogy, and the condition is not left-right symmetric; that is, … See more Definition Let R be ring. Then R is semiperfect if any of the following equivalent conditions hold: See more WebA subclass of clean rings, here called J-clean rings, also known as F-semiperfect rings, is studied. It includes the uniquely clean rings. There is a mono-functor from commutative rings to J-clean rings which satisfies a universal property. Earlier non-functorial ways of embedding rings in J-clean rings can be derived from the functor. olly turmeric