A Note on (m,n) Quasi-Ideals in Semigroups
Moin A. Ansari, Mohd Rais Khan, J. P. Kaushik · 2009
The notion of quasi-ideal is generalization of the notion of one sided ideal. It was introduced by Otto Steinfeld in 1953 for rings (6) and in 1956 for semigroups (7). Quasi-ideals have been the theme of several papers ((4), (5), (2) etc). Furthermore, it has been widely studied in various algebraic structures viz. involution rings, near-rings, regular rings, Γ-Semirings, Lie algebra etc. In this paper, some intersection properties and characterizations of (m,n) quasi-ideals of semigroups has been taken into account. We have also obtained some results for left ideals, right ideals and quasi-ideals of semigroups and regular semigroups. Ideals in this paper have been taken into semigroup theoretical sense.