# 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