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
We introduce the relations Lu and Ru with respect to a subset U of idempotents. Based on Lv and Rv, we define a new class of semigroups which we name U-concordant semigroups. Our purpose is to describe U-concordant se...We introduce the relations Lu and Ru with respect to a subset U of idempotents. Based on Lv and Rv, we define a new class of semigroups which we name U-concordant semigroups. Our purpose is to describe U-concordant semigroups by generalized categories over a regular biordered set. We show that the category of U-concordant semigroups and admissible morphisms is isomorphic to the category of RBS generalized categories and pseudo functors. Our approach is inspired from Armstrong＇s work on the connection between regular biordered sets and concordant semigroups. The significant difference in strategy is by using RBS generalized categories equipped with pre-orders, we have no need to discuss the quotient of a category factored by a congruence.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This research was supported by the NSFC （Grant No. 11471255, 11501331）. The second author was supported by the Shandong Province Natural Science Foundation （Grant No. BS2015SF002）, SDUST Research Fund （No. 2014TDJH102）, and Joint Innovative Center for Safe and Effective Mining Technology and Equipment of Coal Resources, Shandong Province.
文摘We introduce the relations Lu and Ru with respect to a subset U of idempotents. Based on Lv and Rv, we define a new class of semigroups which we name U-concordant semigroups. Our purpose is to describe U-concordant semigroups by generalized categories over a regular biordered set. We show that the category of U-concordant semigroups and admissible morphisms is isomorphic to the category of RBS generalized categories and pseudo functors. Our approach is inspired from Armstrong＇s work on the connection between regular biordered sets and concordant semigroups. The significant difference in strategy is by using RBS generalized categories equipped with pre-orders, we have no need to discuss the quotient of a category factored by a congruence.
