Topological centers of semigroups and semigroup algebras
| dc.contributor.author | Askarisayah, Mehdi | |
| dc.contributor.examiningcommittee | Craigen, Robert (Mathematics) | |
| dc.contributor.examiningcommittee | Clouatre, Raphael (Mathematics) | |
| dc.contributor.supervisor | Zhang, Yong | |
| dc.date.accessioned | 2025-01-13T15:57:28Z | |
| dc.date.available | 2025-01-13T15:57:28Z | |
| dc.date.issued | 2024-12-19 | |
| dc.date.submitted | 2024-12-19T20:38:23Z | en_US |
| dc.degree.discipline | Mathematics | |
| dc.degree.level | Master of Science (M.Sc.) | |
| dc.description.abstract | This thesis investigates the topological centres and Arens regularity of semigroups and their algebras. Following the work of Richard Arens, who introduced two distinct products (the Arens products) on the second dual of Banach algebras, the thesis' main objective is to study the properties of the topological centres of semigroup algebras, particularly focusing on specific types of semigroups such as the bicyclic semigroup and partially bicyclic semigroup. The thesis begins by introducing concepts such as Arens products, topological centres, and semigroups, including their Stone–Cech compactification. Then the thesis explores the Arens irregularity of the bicyclic semigroup S1 and the partially bicyclic semigroups S2 and S1,1. We shall prove that these semigroups are strongly Arens irregular, and that their left topological centres are determined by sets consisting of two points. The study also extends to the measure algebras M(S1), M(S2), and M(S1,1), proving that their left topological centres are similarly determined by sets that consist of two-point. Moreover, this thesis investigates Arens regularity of inverse semigroup algebras. We shall prove that for an inverse semigroup S if E(S) is uniformly locally finite then l1(S) is Arens regular if and only if the maximal subgroups of S are finite, and each D-class has finitely many idempotents. | |
| dc.description.note | February 2025 | |
| dc.identifier.uri | http://hdl.handle.net/1993/38783 | |
| dc.language.iso | eng | |
| dc.subject | Arens Regularity, Semigroup Algebras | |
| dc.title | Topological centers of semigroups and semigroup algebras | |
| local.subject.manitoba | no |