Study of Von Neumann Abelian Regular Rings
Keywords:Abelian regular ring, Strongly regular ring, Injective module, Projective module, von Neumann regular ring.
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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