On (m, n)-ideals and (m, n)-regular ordered semigroups

Abstract

Let m, n be non-negative integers. A subsemigroup A of an ordered semigroup (S,  ,  is called an (m, n)-ideal of S if (i) Am SAn  A, and (ii) if x  A, y  S such that y  x, then y  A. In this paper, necessary and sufficient conditions for every (m, n)-ideal (resp. (m, n)-quasi-ideal) of an (m, n)-ideal (resp. (m, n)-quasi-ideal) A of S is an (m, n)-ideal (resp. (m, n)-quasiideal) of S will be given. Moreover, (m, n)-regularity of S will be discussed. The results obtained extend the results on semigroups (without order) studied by Bogdanovic' (1979).

Keywords

• semigroup
• ordered semigroup
• n)-ideal
• n)-quasi-ideal
• n)-regular