Abstract
The relation in the title is S defined by
on an arbitrary semigroup. We investigate antisymmetry of S by means of a (minimal) family Ϝ whose members can not appear as subsemigroups. Transitivity of S is characterized similarly by means of the family Ϝ and homomorphic images of a certain semigroup. We study the transfer of certain properties of a monoid T and the Bruck semigroup B(T,α) over T. The paper concludes with a consideration of certain properties of the relation S on inverse semigroups.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Vol. I, Math. Surveys No. 7, Amer Math. Soc. (Providence, 1961).
M. P. Drazin, A partial order in completely regular semigroups, J. Algebra, 98 (1986), 362–374.
H. Mitsch, A natural partial order for semigroups, Proc. Amer. Math. Soc., 97 (1986), 384–388.
M. Petrich, Introduction to Semigroups, Merrill (Columbus, 1973).
M. Petrich, Inverse Semigroups, Wiley (New York, 1984).
M. Petrich, Certain partial orders on semigroups, Czechoslovak Math. J., 51 (2001), 415–432.
I. Sussman, A generalization of Boolean rings, Math. Ann., 136 (1958), 326–338.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Petrich, M. A relation for general and inverse semigroups. Acta Mathematica Hungarica 97, 303–322 (2002). https://doi.org/10.1023/A:1021661231635
Issue Date:
DOI: https://doi.org/10.1023/A:1021661231635