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On regularity preservation in a semigroup
| Content Provider | Scilit |
|---|---|
| Author | Hickey, J. B. |
| Copyright Year | 2004 |
| Description | We consider certain subsets of a semigroup S, defined mainly by conditions involving regularity preservation. In particular, the regular base B(S) of S may be regarded as a generalisation of the zero ideal in a semigroup with zero; if it non-empty then S is E-inversive. The other subsets considered are related in a natural way either to B(S) or to the set RP(S) of regularity-preserving elements in S. In a regular semigroup (equipped with the Hartwig-Nambooripad order) each of these subsets contains either minimal elements only or maximal elements only. The relationships between the subsets are discussed, and some characterisations of completely simple semigroups are obtained. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3E868B4DA5C1BD9487474E372618C8FC/S0004972700034274a.pdf/div-class-title-on-regularity-preservation-in-a-semigroup-div.pdf |
| Ending Page | 86 |
| Page Count | 18 |
| Starting Page | 69 |
| ISSN | 00049727 |
| e-ISSN | 17551633 |
| DOI | 10.1017/s0004972700034274 |
| Journal | Bulletin of the Australian Mathematical Society |
| Issue Number | 1 |
| Volume Number | 69 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2004-02-01 |
| Access Restriction | Open |
| Subject Keyword | Bulletin of the Australian Mathematical Society History and Philosophy of Science Subsets Considered Regularity Preservation Characterisations |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
