Study of Von Neumann Abelian Regular Rings

Authors

  • Md Asadujjaman Department of Mathematics, University of Dhaka, Dhaka, Bangladesh
  • Sharmin Alam Department of Computer Science and Engineering, Green University of Bangladesh, Dhaka, Bangladesh
  • Umme Ruman Department of Computer Science and Engineering, Green University of Bangladesh, Dhaka, Bangladesh
  • Shamima Islam Department of Computer Science and Engineering, Green University of Bangladesh, Dhaka, Bangladesh

DOI:

https://doi.org/10.3329/gubjse.v7i0.54013

Keywords:

Abelian regular ring, Strongly regular ring, Injective module, Projective module, von Neumann regular ring.

Abstract

This paper is concerned with the basic properties of a class of regular rings of some "classical" type. Abelian regular rings are, however, a more indirect concept, in that a nontrivial theorem is required to show that strongly regular rings are actually regular. For this reason, we view abelianness as the more natural property. We first collect a number of equivalent characterizations of abelian regular rings, before proving that "abelian regular" is equivalent to "strongly regular".

GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 7, Dec 2020 P 14-20

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Published

2021-07-07

How to Cite

Asadujjaman, M., Alam, S., Ruman, U., & Islam, S. (2021). Study of Von Neumann Abelian Regular Rings. GUB Journal of Science and Engineering, 7, 14–20. https://doi.org/10.3329/gubjse.v7i0.54013

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