SEMIGROUPS SATISFYING RING-LIKE CONDITIONS.
Abstract
A subset R(S) of a semigroup S is introduced and examined under special conditions. Arising from the study is the following characterization: R(S) = S if and only if each element of S has finite order and each idempotent element is a left zero of S. But R(S) = S is equivalent to the condition that S has no modular right congruences different from the universal congruence. Hence, in the setting of automaton theory, R(S) = S if and only if every strictly cyclic automaton over S is isomorphic to S/upsilon, the null automaton of cardinality one. Equivalently, every strictly cyclic automaton over S is the null automaton of cardinality one if and only if each element of S has finite order and each idempotent element is a left zero of S. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1969
- Accession Number
- AD0691257
Entities
People
- Wendell P. Jones
Organizations
- University of Iowa