## One-sided congruences on inverse semigroups

HTML articles powered by AMS MathViewer

- by John Meakin PDF
- Trans. Amer. Math. Soc.
**206**(1975), 67-82 Request permission

## Abstract:

By the kernel of a one-sided (left or right) congruence $\rho$ on an inverse semigroup $S$, we mean the set of $\rho$-classes which contain idempotents of $S$. We provide a set of independent axioms characterizing the kernel of a one-sided congruence on an inverse semigroup and show how to reconstruct the one-sided congruence from its kernel. Next we show how to characterize those partitions of the idempotents of an inverse semigroup $S$ which are induced by a one-sided congruence on $S$ and provide a characterization of the maximum and minimum one-sided congruences on $S$ inducing a given such partition. The final two sections are devoted to a study of indempotent-separating one-sided congruences and a characterization of all inverse semigroups with only trivial full inverse subsemigroups. A Green-Lagrange-type theorem for finite inverse semigroups is discussed in the fourth section.## References

- A. H. Clifford and G. B. Preston,
*The algebraic theory of semigroups. Vol. I*, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR**0132791** - L. M. Gluskin,
*Elementary generalized groups*, Mat. Sb. N. S.**41(83)**(1957), 23–36 (Russian). MR**0090595** - J. M. Howie,
*The maximum idempotent-separating congruence on an inverse semigroup*, Proc. Edinburgh Math. Soc. (2)**14**(1964/65), 71–79. MR**163976**, DOI 10.1017/S0013091500011251 - G. B. Preston,
*Inverse semi-groups*, J. London Math. Soc.**29**(1954), 396–403. MR**64036**, DOI 10.1112/jlms/s1-29.4.396 - N. R. Reilly and H. E. Scheiblich,
*Congruences on regular semigroups*, Pacific J. Math.**23**(1967), 349–360. MR**219646** - Gérard Lallement,
*Demi-groupes réguliers*, Ann. Mat. Pura Appl. (4)**77**(1967), 47–129 (French). MR**225915**, DOI 10.1007/BF02416940

## Additional Information

- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**206**(1975), 67-82 - MSC: Primary 20M10
- DOI: https://doi.org/10.1090/S0002-9947-1975-0369580-9
- MathSciNet review: 0369580