Cross-connections and variants of the full transformation semigroup
Cross-connection theory propounded by Nambooripad describes the ideal structure of a regular semigroup using the categories of principal left (right) ideals. A variant T X of the full transformation semigroup (TX, ·) for an arbitrary θ ∈ TX is the semigroup T X = (TX, ∗) with the binary operation α∗...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
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2018
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| Sorozat: | Acta scientiarum mathematicarum
84 No. 3-4 |
| Kulcsszavak: | Félcsoport, Matematika |
| doi: | 10.14232/actasm-017-044-z |
| Online Access: | http://acta.bibl.u-szeged.hu/56920 |
| Tartalmi kivonat: | Cross-connection theory propounded by Nambooripad describes the ideal structure of a regular semigroup using the categories of principal left (right) ideals. A variant T X of the full transformation semigroup (TX, ·) for an arbitrary θ ∈ TX is the semigroup T X = (TX, ∗) with the binary operation α∗ β = α· θ · β where α, β ∈ TX. In this article, we describe the ideal structure of the regular part Reg(T X) of the variant of the full transformation semigroup using cross-connections. We characterize the constituent categories of Reg(T X) and describe how they are cross-connected by a functor induced by the sandwich transformation θ. This leads us to a structure theorem for the semigroup and gives the representation of Reg(T X) as a cross-connection semigroup. Using this, we give a description of the biordered set and the sandwich sets of the semigroup. |
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| Terjedelem/Fizikai jellemzők: | 377-399 |
| ISSN: | 0001-6969 |