Abstract
In this paper, firstly it is shown that a regular semigroup S becomes a regular *-semigroup (in the sense of [1]) if and only if S has a certain subset called a p-system. Secondly, all the normal *-bands are completely described in terms of rectangular *-bands (square bands) and transitive systems of homomorphisms of rectangular *-bands. Further, it is shown that an orthodox semigroup S becomes a regular *-semigroup if there is a p-system F of the band ES of idempotents of S such that F∋e, ES∋t, e≥t imply t∈F. By using this result, it is also shown that F is a p-system of a generalized inverse semigroup S if and only if F is a p-system of FS.
Similar content being viewed by others
References
Nordahl, T.E. and H.E. Scheiblich,Regular * semigroups, Semigroup Forum 16(1978), 369–377.
Petrich, M.,Introduction to semigroups, A Bell & Howell Company, Columbus, Ohio, 1973.
Reilly, N.R.,A class of regular *-semigroups, Semigroup Forum 18 (1979), 385–386.
Scheiblich, H.E.,The free elementary *orthodox semigroups, Semigroups, edited by T.E. Hall, P.R. Jones and G. B. Preston, Proceedings of the Monash University Conference on Semigroups, Academic Press, 1980.
Scheiblich, H.E.,Projective and injective bands with involution, to appear.
Scheiblich, H.E.,Generalized inverse semigroups with involution, to appear.
Yamada, M.,Regular semigroups whose idempotents satisfy permutation identities, Pacific J. Math. 21 (1967), 371–392.
Yamada, M.,On a certain class of regular semigroups, Symposium on Regular Semigroups, Northern Illinois University, 1979, 146–179.
Author information
Authors and Affiliations
Additional information
Communicated by Boris M. Schein
Dedicated to Professor L. M. Gluskin on his 60th birthday
Rights and permissions
About this article
Cite this article
Yamada, M. P-systems in regular semigroups. Semigroup Forum 24, 173–187 (1982). https://doi.org/10.1007/BF02572766
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02572766