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Ordens parciais em semigrupos
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Abstract(s)
Várias relações em semigrupos arbitrários são frequentemente importantes no estudo da estrutura e propriedades dos semigrupos. Além das relações de Green, que são de fato equivalências, o mais notável é a ordem parcial natural nos semigrupos regulares, ordem que posteriormente foi estendida a semigrupos em geral. Naturalmente, outras podem ser introduzidas e ao tentarmos provar propriedades sobre elas somos naturalmente levados a novas classes de semigrupos, cuja estrutura resulta de determinadas propriedades satisfeitas por tais relações.
Drazin [4] fez uma revisão sistemática de algumas destas relações, mas para nós são relevantes C, S e N. Consideramos também a relação introduzida por Mitsch [7] como uma generalização da ordem parcial natural para semigrupos regulares introduzida por Hartwig [5] e Nambooripad [8].
O objetivo deste trabalho é descrever classes de semigrupos onde estas várias
Relações coincidem ou têm determinadas propriedades (como compatibilidade com o produto, etc.).
Frequently, several relations in arbitrary semigroups are relevant for the study of those semigroups’ properties and structure. Besides Green’s relations, which are equivalence relations, the most notable is the natural partial order in regular semigroups, which was later extended to general semigroups. Naturally, other relations can be introduced, and when we attempt to prove their properties we are lead to new semigroup classes, whose structure results from certain properties satisfied by those relations. Drazin [4] did a systematic review of some of these relations, but we will consider particularly C, S e N. We also consider the relation introduced by Mitsch [7] as a generalization of the natural partial order for regular semigroups introduced by Hartwig [5] and Nambooripad [8]. The purpose of this dissertation is to describe semigroup classes where these various relation coincide or exhibit certain properties (such as compatibility with multiplication, etc.).
Frequently, several relations in arbitrary semigroups are relevant for the study of those semigroups’ properties and structure. Besides Green’s relations, which are equivalence relations, the most notable is the natural partial order in regular semigroups, which was later extended to general semigroups. Naturally, other relations can be introduced, and when we attempt to prove their properties we are lead to new semigroup classes, whose structure results from certain properties satisfied by those relations. Drazin [4] did a systematic review of some of these relations, but we will consider particularly C, S e N. We also consider the relation introduced by Mitsch [7] as a generalization of the natural partial order for regular semigroups introduced by Hartwig [5] and Nambooripad [8]. The purpose of this dissertation is to describe semigroup classes where these various relation coincide or exhibit certain properties (such as compatibility with multiplication, etc.).
Description
Keywords
Semigrupos (matemática) Matemática
Pedagogical Context
Citation
Matavele, Carlos Casimiro - Ordens parciais em semigrupos [Em linha]. [S.l.]: [s.n.], 2017. 30 f.