Melanija Mitrović

Semigroups with apartness

Proving a constructive version of the Spectral Mapping Theorem, Bridges and Havea used a constructive semigroup with inequality in [8]. This motivated us to achieve a little progress in that direction. The starting point is the structure called a semigroup with apartness. Our primary objective is to prove isomorphism theorems for such constructive semigroups. In doing so our main ideas and notions come from [10].

SEMIGROUPS SATISFYING CERTAIN REGULARITY CONDITIONS

S. Bogdanovic, M. Ciric, P. Stanimirovic and T. Petkovic in [4] proved that every regularity condition on semigroups is equivalent to one of the 14 conditions given here in Figure 1. Semigroups satisfying some of these conditions were studied only from the ideal-theoretical point of view, by S. Lajos and G. Szasz in [11]. The purpose of this paper is to describe the structure and give some new ideal-theoretical characterizations of these semigroups.