ON STRONGLY REGULAR NEAR-SUBTRACTION SEMIGROUPS

Title & Authors
ON STRONGLY REGULAR NEAR-SUBTRACTION SEMIGROUPS
Dheena, P.; Kumar, G. Satheesh;

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 $\small{\in}$ X (ii) If P is a prime ideal of X, then there exists no proper k-ideal M such that P $\small{\subset}$ M (iii) Every ideal I of X fulfills \$I
Keywords
subtraction semigroup;near-subtraction semigroup;regular;strongly regular;
Language
English
Cited by
1.
WEAKLY PRIME LEFT IDEALS IN NEAR-SUBTRACTION SEMIGROUPS,;;

대한수학회논문집, 2008. vol.23. 3, pp.325-331
References
1.
J. C. Abbott, Sets, Lattices and Boolean Algebras, Allyn and Bacon, Boston, 1969

2.
J. C. Beidleman, A note on Regular near-rings, J. Indian Math. Soc. 33 (1969), 207-210

3.
J. R. Clay, The near-rings on groups of low order, Math. Z. 104 (1968), 364-371

4.
K. H. Kim, On Subtraction Semiqroups, Scientiae Mathematicae Japonicae 62 (2005), no. 2, 273-280

5.
Meldrum, Varieties and d.g. near-rings, Proc. Edinburgh Math. Soc. (series 1) 17 (1971), 271-274

6.
G. Mason, Strongly regular near-rings, Proc. Edinburgh Math. Soc. 23 (1980), 27-35

7.
G. Pilz, Near-rings, North-Holland, Amsterdam, 1983

8.
E. H. Roh, K. H. Kim, and Jong Geol Lee, On Prime and Semiprime ideals in Subtraction Semiqroups, Scientiae Mathematicae Japonicae 61 (2005), no. 2, 259-266

9.
B. M. Schein, Difference Semiqroups, Communications in algebra 20 (1992), 2153-2169

10.
B. Zelinka, Subtraction Semigroups, Math. Bohemica 120 (1995), 445-447