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Representations of inverse semigroups in complete atomistic inverse meet-semigroups
Citation
FitzGerald, DG, Representations of inverse semigroups in complete atomistic inverse meet-semigroups, Semigroup Forum, 101 pp. 87-101. ISSN 0037-1912 (2020) [Refereed Article]
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Copyright Statement
Copyright 2020 Springer Nature Switzerland AG
DOI: doi:10.1007/s00233-020-10091-9
Abstract
As an appropriate generalisation of the features of the classical (Schein) theory of representations of inverse semigroups in I 𝑋, a theory of representations of inverse semigroups by homomorphisms into complete atomistic inverse ∧-semigroups is developed. This class of inverse ∧-semigroups, otherwise known as inverse algebras, includes partial automorphism monoids of entities such as graphs, vector spaces and modules. A workable theory of decompositions is reached; however complete distributivity is required for results approaching those of the classical case.
Item Details
| Item Type: | Refereed Article |
|---|---|
| Keywords: | Inverse semigroups; Representation of semigroups; Inverse meet semigroups; Partial automorphism monoids |
| Research Division: | Mathematical Sciences |
| Research Group: | Pure mathematics |
| Research Field: | Group theory and generalisations |
| Objective Division: | Expanding Knowledge |
| Objective Group: | Expanding knowledge |
| Objective Field: | Expanding knowledge in the mathematical sciences |
| UTAS Author: | FitzGerald, DG (Dr Des FitzGerald) |
| ID Code: | 140879 |
| Year Published: | 2020 |
| Deposited By: | Mathematics |
| Deposited On: | 2020-09-14 |
| Last Modified: | 2020-10-29 |
| Downloads: | 11 View Download Statistics |
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