|
| << vorige | volgende >> |
Tijdschrift beschrijving
Alle jaargangen van het bijbehorende tijdschrift
Alle afleveringen van het bijbehorende jaargang
Alle artikelen van de bijbehorende aflevering
Details van artikel 8 van 25 gevonden artikelen
| Titel: |
Fundamental Representations for Classes of Semigroups Containing a Band of Idempotents |
| Auteur: |
Qallali, Abdulsalam El Fountain, John Gould, Victoria |
| Verschenen in: |
Communications in algebra |
| Paginering: | Jaargang 36 (2008) nr. 8 pagina's 2998-3031 |
| Jaar: |
2008-08 |
| Inhoud: |
The construction by Hall of a fundamental orthodox semigroup WB from a band B provides an important tool in the study of orthodox semigroups. Hall's semigroup WB has the property that a semigroup is fundamental and orthodox with band of idempotents isomorphic to B if and only if it is embeddable as a full subsemigroup into WB. The aim of this article is to extend Hall's approach to some classes of nonregular semigroups. From a band B, we construct a semigroup UB that plays the role of WB for a class of weakly B-abundant semigroups having a band of idempotents B. The semigroups we consider, in particular UB, must also satisfy a weak idempotent connected condition. We show that UB has subsemigroup VB where VB satisfies a stronger notion of idempotent connectedness, and is again the canonical semigroup of its kind. In turn, VB contains WB as its subsemigroup of regular elements. Thus we have the following inclusions as subsemigroups: [image omitted] either of which may be strict, even in the finite case. The existence of the semigroups UB and VB enable us to prove a structure theorem for classes of weakly B-abundant semigroups having band of idempotents B, and satisfying either of our idempotent connected conditions, as spined products of UB, or VB, with a weakly B/D-ample semigroup. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 8 van 25 gevonden artikelen
| << vorige | volgende >> |