Translational hulls of semigroups of endomorphisms of an algebra
Victoria Gould, Ambroise Grau, Marianne Johnson, Mark Kambites

TL;DR
This paper studies the structure of translational hulls of subsemigroups of endomorphism monoids in universal algebras, establishing conditions for their realizations and connections to idealisers, with applications to various algebraic structures.
Contribution
It provides new conditions for realizing bi-translations as endomorphisms and links translational hulls to idealisers, extending prior work to broader algebraic contexts.
Findings
Conditions for bi-translation realization as endomorphisms
Isomorphisms between translational hulls and idealisers
Methodology for analyzing translational hulls via quotients
Abstract
We consider the translational hull of an arbitrary subsemigroup of an endomorphism monoid where is a universal algebra. We give conditions for every bi-translation of to be realised by transformations, or by endomorphisms, of . We demonstrate that certain of these conditions are also sufficient to provide natural isomorphisms between the translational hull of and the idealiser of within , which in the case where is an ideal is simply . We describe the connection between these conditions and work of Petrich and Gluskin in the context of densely embedded ideals. Where the conditions fail, we develop a methodology to extract information concerning from the translational hull of a quotient of . We illustrate these concepts in detail in the cases where…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicssemigroups and automata theory · Fuzzy and Soft Set Theory · Advanced Control Systems Optimization
