Von Neumann Regular and Related Elements in Commutative Rings-Reference-Cited by-同舟云学术

Von Neumann Regular and Related Elements in Commutative Rings

Published:2012-10-31 Issue:spec01 Volume:19 Page:1017-1040
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Anderson David F.¹,Badawi Ayman²

Affiliation:

1. Department of Mathematics, The University of Tennessee, Knoxville, TN 37996-1320, USA

2. Department of Mathematics & Statistics, The American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates

Abstract

Let R be a commutative ring with nonzero identity. In this paper, we study the von Neumann regular elements of R. We also study the idempotent elements, π-regular elements, the von Neumann local elements, and the clean elements of R. Finally, we investigate the subgraphs of the zero-divisor graph Γ(R) of R induced by the above elements.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1005386712000831

Reference28 articles.

1. Combining Local and Von Neumann Regular Rings

2. COMMUTATIVE RINGS WHOSE ELEMENTS ARE A SUM OF A UNIT AND IDEMPOTENT

3. Idealization of a Module

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