ON SOME CLASSES OF H-SEMIGROUPS.
Abstract
The report further develops the study of H-semigroups introduced by R.H. Oehmke. Several characterizations arise which make possible the identification of maximal modular congruences. A semigroup S is an inverse H-semigroup if and only if S is a semilattice of disjoint Hamiltonian groups. From this it follows that sigma is a maximal modular congruence on S if and only if S/sigmais a cyclic group of prime order or S/sigma = (0,1). In the setting of automaton theory, sigma is a maximal modular congruence on S if and only if its related automaton is either strongly connected or strongly irreducible and of cardinality two. For each idempotent e of S there is a maximal modular congruence sigma on S such that its related automaton is strongly irreducible and of cardinality two with sigma sub e as a strict generator where e is the minimum idempotent in sigma e. S is t-semisimple if and only if for each nonidempotent element g of S there is a maximal modular congruence sigma on S such that its related automaton is strongly connected and has sigma sub g as a strict generator. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1970
- Accession Number
- AD0708420
Entities
People
- Mary Joel Jordan
Organizations
- University of Iowa