Semiperfect ring
WebWe call C a Krull–Schmidt category provided that every object decomposes into a finite direct sum of objects having local endomorphism rings. Equivalently, C has split idempotents and the endomorphism ring of every object is semiperfect . Properties [ edit] One has the analogue of the Krull–Schmidt theorem in Krull–Schmidt categories: 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.
Semiperfect ring
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WebJan 10, 2024 · Download PDF Abstract: We define topologically semiperfect (complete, separated, right linear) topological rings and characterize them by equivalent conditions. We show that the endomorphism ring of a module, endowed with the finite topology, is topologically semiperfect if and only if the module is decomposable as an (infinite) direct … WebFeb 9, 2024 · It can be shown that there are rings which are left perfect, but not right perfect. However being semiperfect is left-right symmetric property. Some examples of …
WebJan 1, 2024 · In particular, as a direct application, we prove that the commutative group ring RG is J-rad clean if, and only if, R is a commutative J-rad clean ring and G is a torsion abelian group,... 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.
WebNov 20, 2024 · The aim of this paper is to prove the following theorem: Let R be a semiperfect ring. Let Q be a left R -module satisfying (a) Q is R -projective and (b) J (Q) is small in Q. Then Q is projective. Type Research Article Information Canadian Mathematical Bulletin , Volume 24 , Issue 3 , 01 September 1981 , pp. 365 - 367 WebApr 17, 2009 · In 1999 Nicholson asked whether every semiperfect ring is strongly clean and whether the matrix ring of a strongly clean ring is strongly clean. In this paper, we prove that if R = {m / n ∈ ℚ: n is odd}, then M 2 (R) is a semiperfect ring but not strongly clean. Thus, we give negative answers to both questions.
WebSemiperfect rings are rings which possess two properties of artinian rings that are crucial for the Krull{Schmidt theory: a ring Ris semiperfect (cf. [9, Ch. 8]) if (a) R=J(R) is …
WebJan 10, 2024 · Abstract: We define topologically semiperfect (complete, separated, right linear) topological rings and characterize them by equivalent conditions. We show that … staybridge suites cranberry twp paWebSep 21, 2016 · The structure of an Abelian ring R is completely determined in relation with the local property when X ( R) is a union of 2; 3; 4; and 5 orbits under the left regular action on X ( R) by G ( R ): For a semiperfect ring R which is not local, it is shown that if G ( R) is a cyclic group with 2 ∈ G ( R ); then R is finite. staybridge suites corpus christi texasWebAug 11, 2024 · semiperfect ring symmetric ring π -regular ring 2024 MATHEMATICS SUBJECT CLASSIFICATION: 16U80 16U60 16D25 16S50 16N40 Acknowledgments The authors thank the referee for very careful reading of the manuscript and many valuable suggestions that improved the paper by much. Additional information Funding staybridge suites cranberryWebJul 18, 2013 · Here we prove that, for a -primal ring R, the Laurent series ring x is a clean ring if and only if R is a semiregular ring with J R nil. This disproves the claim in K. I. Sonin [‘Semiprime and semiperfect rings of Laurent series’, Math. Notes 60 (1996), 222–226] that the Laurent series ring over a clean ring is again clean. staybridge suites cranbury an ihg hotelWeb开馆时间:周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 staybridge suites dearborn mi phone numberWebJul 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 staybridge suites cranbury new jerseyWebOct 4, 2014 · A semi-perfect ring may also be characterized by the condition that every module admits a direct decomposition with respect to which the maximal direct … staybridge suites customer service