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On congruence compact monoids
Author(s) -
Bulman-Fleming S.,
Hotzel E.,
Normak P.
Publication year - 1999
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300007701
Subject(s) - congruence (geometry) , mathematics , pure mathematics , commutative property , intersection (aeronautics) , algebra over a field , geometry , engineering , aerospace engineering
A universal algebra is called congruence compact if every family of congruence classes with the finite intersection property has a non‐empty intersection. This paper determines the structure of all right congruence compact monoids S for which Green's relations ℐ and ℋ coincide. The results are thus sufficiently general to describe, in particular, all congruence compact commutative monoids and all right congruence compact Clifford inverse monoids.