In this paper, for an arbitrary regular biordered set E, by usingbiorder-isomorphisms between the ω-ideals of E, we construct a fundamental regular semigroup W_Ecalled NH-semigroup of E, whose idempotent biordered se...In this paper, for an arbitrary regular biordered set E, by usingbiorder-isomorphisms between the ω-ideals of E, we construct a fundamental regular semigroup W_Ecalled NH-semigroup of E, whose idempotent biordered set is isomorphic to E. We prove further thatW_E can be used to give a new representation of general regular semigroups in the sense that, forany regular semigroup S with the idempotent biordered set isomorphic to E, there exists ahomomorphism from S to W_E whose kernel is the greatest idempotent-separating congruence on S andthe image is a full symmetric subsemigroup of W_E. Moreover, when E is a biordered set of asemilattice E_0, W_E is isomorphic to the Munn-semigroup T_(E_0); and when E is the biordered set ofa band B, W_E is isomorphic to the Hall-semigroup W_B.展开更多
In this paper, a special kind of partial algebras called projective partial groupoids is defined. It is proved that the inverse image of all projections of a fundamental weak regular *-semigroup under the homomorphism...In this paper, a special kind of partial algebras called projective partial groupoids is defined. It is proved that the inverse image of all projections of a fundamental weak regular *-semigroup under the homomorphism induced by the maximum idempotent-separating congruence of a weak regular *-semigroup has a projective partial groupoid structure. Moreover, a weak regular *-product which connects a fundamental weak regular *-semigroup with corresponding projective partial groupoid is defined and characterized. It is finally proved that every weak regular *-product is in fact a weak regular *-semigroup and any weak regular *-semigroup is constructed in this way.展开更多
文摘In this paper, for an arbitrary regular biordered set E, by usingbiorder-isomorphisms between the ω-ideals of E, we construct a fundamental regular semigroup W_Ecalled NH-semigroup of E, whose idempotent biordered set is isomorphic to E. We prove further thatW_E can be used to give a new representation of general regular semigroups in the sense that, forany regular semigroup S with the idempotent biordered set isomorphic to E, there exists ahomomorphism from S to W_E whose kernel is the greatest idempotent-separating congruence on S andthe image is a full symmetric subsemigroup of W_E. Moreover, when E is a biordered set of asemilattice E_0, W_E is isomorphic to the Munn-semigroup T_(E_0); and when E is the biordered set ofa band B, W_E is isomorphic to the Hall-semigroup W_B.
基金Subject supported by NNSF of China (60002007)NSF of Guangdong China (011438)
文摘In this paper, a special kind of partial algebras called projective partial groupoids is defined. It is proved that the inverse image of all projections of a fundamental weak regular *-semigroup under the homomorphism induced by the maximum idempotent-separating congruence of a weak regular *-semigroup has a projective partial groupoid structure. Moreover, a weak regular *-product which connects a fundamental weak regular *-semigroup with corresponding projective partial groupoid is defined and characterized. It is finally proved that every weak regular *-product is in fact a weak regular *-semigroup and any weak regular *-semigroup is constructed in this way.
