Right group congruences on a semigroup

Author:
Francis E. Masat

Journal:
Proc. Amer. Math. Soc. **50** (1975), 107-114

MSC:
Primary 20M10

MathSciNet review:
0372085

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper develops necessary and sufficient conditions on an algebraic semigroup in order that it will have nontrivial right group homomorphic images. A central notion used is that of how the normal subsemigroups associated with the group images of relate to the right group images of . The results presented thus extend those of R. R. Stoll. Where right group congruences exist, the structure of is determined and the right group congruences are characterized in terms of group congruences and right zero congruences on . Sufficient conditions are then found for the existence of a minimum right group congruence on , and isomorphic right group congruences and the minimum right group congruence on are described. Lastly, an application is made to regular semigroups whose idempotents form a rectangular band.

**[1]**A. H. Clifford and G. B. Preston,*The algebraic theory of semigroups. Vol. II*, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1967. MR**0218472****[2]**-,*The algebraic theory of semigroups*. Vol. II, Math. Surveys, no. 7, Amer. Math. Soc., Providence, R.I., 1961. MR**36**#1558.**[3]**J. M. Howie and G. Lallement,*Certain fundamental congruences on a regular semigroup*, Proc. Glasgow Math. Assoc.**7**(1966), 145–159. MR**0197598****[4]**Francis E. Masat,*Right group and group congruences on a regular semigroup*, Duke Math. J.**40**(1973), 393–402. MR**0318378****[5]**R. R. Stoll,*Homomorphisms of a semigroup onto a group*, Amer. J. Math.**73**(1951), 475–481. MR**0041128**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
20M10

Retrieve articles in all journals with MSC: 20M10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0372085-8

Keywords:
Right group congruences,
ideal decompositions,
orthodox semigroups,
right zero congruences,
normal subsemigroups,
group congruences

Article copyright:
© Copyright 1975
American Mathematical Society