Aufsatz in einer Fachzeitschrift
Associativity of the regular semidirect product of existence varieties
Details zur Publikation
Autor(inn)en: | Billhardt, B.; Szendrei, M. |
Publikationsjahr: | 2000 |
Zeitschrift: | Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics |
Seitenbereich: | 85-115 |
Jahrgang/Band : | 69 |
ISSN: | 0263-6115 |
eISSN: | 2396-8192 |
DOI-Link der Erstveröffentlichung: |
URN / URL: |
Zusammenfassung, Abstract
The associativity of the regular semidirect product of existence varieties introduced by Jones and Trotter was proved under certain conditions by Reilly and Zhang. Here we establish associativity in many new cases. Moreover, we prove that the regular semidirect product is right distributive with respect to the join operation. In particular, both associativity and right distributivity yield within the varieties of completely simple semigroups. Analogous results are obtained for e-pseudovarieties of finite regular semigroups.
The associativity of the regular semidirect product of existence varieties introduced by Jones and Trotter was proved under certain conditions by Reilly and Zhang. Here we establish associativity in many new cases. Moreover, we prove that the regular semidirect product is right distributive with respect to the join operation. In particular, both associativity and right distributivity yield within the varieties of completely simple semigroups. Analogous results are obtained for e-pseudovarieties of finite regular semigroups.
