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ON STRONGLY REGULAR NEAR-SUBTRACTION SEMIGROUPS

  • Dheena, P. (DEPARTMENT OF MATHEMATICS ANNAMALAI UNIVERSITY) ;
  • Kumar, G. Satheesh (DEPARTMENT OF MATHEMATICS ANNAMALAI UNIVERSITY)
  • Published : 2007.07.31

Abstract

In this paper we introduce the notion of strongly regular near-subtraction semigroups (right). We have shown that a near-subtraction semigroup X is strongly regular if and only if it is regular and without non zero nilpotent elements. We have also shown that in a strongly regular near-subtraction semigroup X, the following holds: (i) Xa is an ideal for every a $\in$ X (ii) If P is a prime ideal of X, then there exists no proper k-ideal M such that P $\subset$ M (iii) Every ideal I of X fulfills $I=I^2$.

Keywords

subtraction semigroup;near-subtraction semigroup;regular;strongly regular

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