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) : Jones,Wendell P.

Report Date : MAY 1969

Pagination or Media Count : 58

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)

Descriptors :   (*RINGS(MATHEMATICS), GROUPS(MATHEMATICS)), (*GROUPS(MATHEMATICS), AUTOMATA), SET THEORY, THEOREMS

Subject Categories : Theoretical Mathematics
      Bionics

Distribution Statement : APPROVED FOR PUBLIC RELEASE