On semigroups in which every Rees one-sided congruence is a congruence |
| |
Authors: | G Baird G Thierrin |
| |
Institution: | (1) University of Western Ontario, London, Canada |
| |
Abstract: | The purpose of this paper is to examine the structure of those semigroups which satisfy one or both of the following conditions:
Ar(Aℓ): The Rees right (left) congruence associated with any right (left) ideal is a congruence.
The conditions Ar and Aℓ are generalizations of commutativity for semigroups. This paper is a continuation of the work of Oehmke 5] and Jordan 4]
on H-semigroups (H for hamiltonian, a semigroup is called an H-semigroup if every one-sided congruence is a two-sided congruence).
In fact the results of section 2 of Oehmke 5] are proved here under the condition Ar and/or Aℓ and not the stronger hamiltonian condition.
Section 1 of this paper is essentially a summary of the known results of Oehmke. In section 2 we examine the structure of
irreducible semigroups satisfying the condition Ar and/or Aℓ. In particular we determine all regular (torsion) irreducible semigroups satisfying both the conditions Ar and Aℓ.
This research has been supported by Grant A7877 of the National Research Council of Canada. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|