A Note on GP-Injectivity-Reference-Cited by-同舟云学术

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A Note on GP-Injectivity

Published:2009-12 Issue:04 Volume:16 Page:625-629
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Hirano Yasuyuki¹,Kim Hong Kee²,Kim Jin Yong³

Affiliation:

1. Department of Mathematics, Naruto University of Education, 748, Nakashima, Takashima, Naruto-cho, Naruto-shi 772-8502, Japan

2. Department of Mathematics and RINGS, Gyeongsang National University, Jinju 660-701, Korea

3. Department of Mathematics and Institute of Natural Sciences, Kyung Hee University, Suwon 446-701, Korea

Abstract

New characteristic properties of left GPGV-rings are given. It is shown that if R is a left GPGV-ring, then for any nonzero element a in R, there is a positive integer n such that an≠ 0 and (RaR+ l(an))⊕ L=R for some left ideal L contained in Soc (RR). As a corollary of this result, we are able to give a positive answer to a question raised by Yue Chi Ming.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1005386709000583

Reference14 articles.

1. A Class of Rings Having All Singular Simple Modules Injective.

2. GP-Injective Rings Need Not be P-Injective

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