Accession Number:
AD0691257
Title:
SEMIGROUPS SATISFYING RING-LIKE CONDITIONS.
Descriptive Note:
Technical rept.,
Corporate Author:
IOWA UNIV IOWA CITY DEPT OF MATHEMATICS
Personal Author(s):
Report Date:
1969-05-01
Pagination or Media Count:
58.0
Abstract:
A subset RS of a semigroup S is introduced and examined under special conditions. Arising from the study is the following characterization RS S if and only if each element of S has finite order and each idempotent element is a left zero of S. But RS 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, RS S if and only if every strictly cyclic automaton over S is isomorphic to Supsilon, 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
Descriptors:
Subject Categories:
- Theoretical Mathematics
- Bionics