Abstract
The aim of this article is to provide structure theorems for weakly B-abundant semigroups satisfying the Congruence Condition (C), where B is a band. Such semigroups may be thought of as generalisations of orthodox semigroups. Our focus is on providing a description of a weakly B-abundant semigroup S with (C) as a spined product of a weakly B-abundant semigroup SB (depending only on B) and S/γB, where γB is the analogue of the least inverse congruence on an orthodox semigroup. This result is an analogue of the Hall-Yamada theorem for orthodox semigroups. In the case that B is a normal band, or S is weakly B-superabundant, we find a closed form for γB. In addition, we build on an existing result of Ren to show that a weakly B-superabundant semigroup (C) is a semilattice of rectangular bands of monoids.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.