The Journal of the Indian Mathematical Society

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Regular Near-Rings


Affiliations
1 University of Southwestern Louisiana, Lafayette, Louisiana, United States
     

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The concept of a regular near-ring was introduced in 1968 by J.C. Beidleman [1]. Strictly analogous to the ring theoretic concept we say a (left) near-ring R is von Neumann regular (or for simplicity, regular) if for each x ∈ R there exists x' ∈ R such that xx'x = x. Ligh [8] was the first to give some structure theory for regular near-rings.
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  • Regular Near-Rings

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Authors

Henry E. Heatherly
University of Southwestern Louisiana, Lafayette, Louisiana, United States

Abstract


The concept of a regular near-ring was introduced in 1968 by J.C. Beidleman [1]. Strictly analogous to the ring theoretic concept we say a (left) near-ring R is von Neumann regular (or for simplicity, regular) if for each x ∈ R there exists x' ∈ R such that xx'x = x. Ligh [8] was the first to give some structure theory for regular near-rings.