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1.
汪立民  张静 《数学进展》2004,33(1):123-124
In 1966, Reilly Characterized bisimple ω-semigroups as Bruck-Reilly extensions of Groups.Later, Munn and Reilly proved that a congruence on a bisimple ω-semigroup is a group congruence or is idempotent-separating. Many author investigated the congruences on Bruck-Reilly ex-  相似文献   

2.
汪立民  商宇 《数学进展》2008,37(1):121-122
The regular semigroups S with an idempotent set Es = {e0,e1,…,en,…} such that e0 > e1 >…> en >… is called a regular ω-semigroup. In [5] Reilly determined the structure of a regular bisimple ω-semigroup as BR(G,θ),which is the classical Bruck-Reilly extension of a group G.  相似文献   

3.
The investigation of U-ample ω-semigroups is initiated. After obtaining some properties of such semigroups, a structure of U-ample ω-semigroups is established. It is proved that a semigroup is a U-ample ω-semigroup if and only if it can be expressed by WBR(T, 0), namely, the weakly Bruck-Reilly extensions of a monoid T. This result not only extends and amplifies the structure theorem of bisimple inverse ω-semigroups given by N. R. Reilly, but also generalizes the structure theorem of ,-bisimple type A ω-semigroups given by U. Asibong-Ibe in 1985.  相似文献   

4.
In this paper, the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal MS-algebras (see [13]). They show that every congruence relation θ on a decomposable MS-algebra L can be uniquely determined by a congruence pair (θ1, θ2), where θ1 is a congruence on the de Morgan subalgebra L?? of L and θ2 is a lattice congruence on the sublattice D(L) of L. They obtain certain congruence pairs of a decomposable MS-algebra L via central elements of L. Moreover, they characterize the permutability of congruences and the strong extensions of decomposable MS-algebras in terms of congruence pairs.  相似文献   

5.
Let P = E G be a Zappa-Szp product of a semilattice E with an identity and a group G. In this paper, we first introduce the concept of congruence pairs for P , and then prove that every congruence on P can be described by such a congruence pair. In fact the congruence lattice on P is lattice-isomorphic to the set of all congruence pairs for P . Finally,we characterize group congruences on P .  相似文献   

6.
In this paper, a complete congruence on the congruence lattice of regular semigroups with Q-inverse transversals is analysed. The classes of this complete congruence which are intervals are discussed and their least and greatest elements are presented clearly.  相似文献   

7.
In this paper we study the isomorphisms of two regular bisimple ω2-semigroups and obtain a criterion for two such semigroups to be isomorphic.  相似文献   

8.
In this paper we study the isomorphisms of two regular bisimple ω2- semigroups and obtain a criterion for two such semigroups to be isomorphic.  相似文献   

9.
The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces.More precisely, it is shown that(1) if(M, ω) admits a Hamiltonian S~1-action, then there exists a two-sphere S in M with positive symplectic area satisfying c1(M, ω), [S] 0,and(2) if the action is non-Hamiltonian, then there exists an S~1-invariant symplectic2-torus T in(M, ω) such that c1(M, ω), [T] = 0. As applications, the authors give a very simple proof of the following well-known theorem which was proved by Atiyah-Bott,Lupton-Oprea, and Ono: Suppose that(M, ω) is a smooth closed symplectic manifold satisfying c1(M, ω) = λ· [ω] for some λ∈ R and G is a compact connected Lie group acting effectively on M preserving ω. Then(1) if λ 0, then G must be trivial,(2) if λ = 0, then the G-action is non-Hamiltonian, and(3) if λ 0, then the G-action is Hamiltonian.  相似文献   

10.
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