As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated by El-Qallali and Fountain. As an analogy of the type W semigroups in the class of abundant se...As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated by El-Qallali and Fountain. As an analogy of the type W semigroups in the class of abundant semigroups, we introduce the U-orthodox semigroups. It is shown that the maximum congruence μ contained in on U-orthodox semigroups can be determined. As a consequence, we show that a U-orthodox semigroup S can be expressed by the spined product of a Hall semigroup W U and a V-ample semigroup (T,V). This theorem not only generalizes a known result of Hall-Yamada for orthodox semigroups but also generalizes another known result of El-Qallali and Fountain for type W semigroups.展开更多
Let 5 be an orthodox semigroup and γ the least inverse congruence on 5. C(S) denotes the set of all congruences on S. In this paper we introduce the concept of admissible triples for S, where admissible triples are c...Let 5 be an orthodox semigroup and γ the least inverse congruence on 5. C(S) denotes the set of all congruences on S. In this paper we introduce the concept of admissible triples for S, where admissible triples are constructed by the congruences on S/γ , the equivalences on E(S)/L and E(S)/R. The notation Ca(S) denotes the set of all admissible triple for S. We prove that every congruence ρ on S can be uniquely determined by the admissible triple induced by ρ, and there exists a lattice isomomorphism between C(S) and Ca(S).展开更多
In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by nsing the equivalences on S/L, S/R and the special congruences on S. Also, such...In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by nsing the equivalences on S/L, S/R and the special congruences on S. Also, such congruence triples are characterized so that an associated congruence can be uniquely determined by a given congruence triple. Moreover, we also consider the VH-congruence pairs on an orthocryptogroup.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 10671151)Natural Science Foundation of Shaanxi Province (Grant No. SJ08A06)partially by UGC (HK) (Grant No. 2160123)
文摘As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated by El-Qallali and Fountain. As an analogy of the type W semigroups in the class of abundant semigroups, we introduce the U-orthodox semigroups. It is shown that the maximum congruence μ contained in on U-orthodox semigroups can be determined. As a consequence, we show that a U-orthodox semigroup S can be expressed by the spined product of a Hall semigroup W U and a V-ample semigroup (T,V). This theorem not only generalizes a known result of Hall-Yamada for orthodox semigroups but also generalizes another known result of El-Qallali and Fountain for type W semigroups.
基金The NNSF (19970128) of China and the NSF ((011438), (021073), (Z02017)) of Guangdong Province.
文摘Let 5 be an orthodox semigroup and γ the least inverse congruence on 5. C(S) denotes the set of all congruences on S. In this paper we introduce the concept of admissible triples for S, where admissible triples are constructed by the congruences on S/γ , the equivalences on E(S)/L and E(S)/R. The notation Ca(S) denotes the set of all admissible triple for S. We prove that every congruence ρ on S can be uniquely determined by the admissible triple induced by ρ, and there exists a lattice isomomorphism between C(S) and Ca(S).
基金Supported by National Natural Science Foundation of China （Grant No. 10571061）
文摘In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by nsing the equivalences on S/L, S/R and the special congruences on S. Also, such congruence triples are characterized so that an associated congruence can be uniquely determined by a given congruence triple. Moreover, we also consider the VH-congruence pairs on an orthocryptogroup.
