The structure of $\omega$-regular semigroups

Janet Ault, Mario Petrich
1971 Bulletin of the American Mathematical Society  
1. Finding the complete structure of regular semigroups of a certain class has succeeded only when sufficiently strong conditions on idempotents and/or ideals have been imposed. On the one hand, there is the theorem of Rees [7], giving the structure of completely 0-simple semigroups, and its successive generalizations to primitive regular semigroups [2], and 3-and 3i-regular semigroups [4]. On the other hand, with very different restrictions, Reilly [8] has determined the structure of bisimple
more » ... o-semigroups, Kocin [l] of inverse simple co-semigroups, Munn [5] of inverse co-semigroups. An co-chain with zero is a poset {e»| i §:0} U0 with ei>e 3 -if i Gi> • • • >Gd-u and cr be a homomorphism of V into G 0 . Let w\A->{0, 1, • • -, d~-1} be any function, denoted by wla-w a . For a£i, O^i, j<d, define (ce, i) by (a, i) =s w a + i (mod d), 0 ^ {a, i) < d, and define [i, a, j] to satisfy [h *,j]d = (i -j) -((a, i) -<a,i».
doi:10.1090/s0002-9904-1971-12677-0 fatcat:ieosz3ue3ve5bam4t2ekjxpvma