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1.
Regular congruences on an E-inversive semigroup 总被引:1,自引:0,他引:1
2.
The congruence extension property (CEP) of semigroups has been extensively studied by a number of authors. We call a compact semigroup S an Ω-compact semigroup if the set of all regular elements of S forms an ideal of S. In this note, we characterize the Ω-compact semigroup having (CEP). Our result extends a recent result obtained by X.J. Guo on the congruence extension property of strong Ω-compact semigroups which is a semigroup containing precisely one regular D-class. 相似文献
3.
Karen D. Aucoin 《Semigroup Forum》1996,52(1):157-162
A topological semigroupS is said to have thecongruence extension property (CEP) provided that for each closed subsemigroupT ofS and each closed congruence σ onT, σ can be extended to a closed congruence
onS. (That is,
∩(T xT=σ). The main result of this paper gives a characteriation of Γ-compact commutative archimedean semigroups with the congruence
extension property (CEP). Consideration of this result was motivated by the problem of characterizing compact commutative
semigroups with CEP as follows. It is well known that every commutative semigroup can be expressed as a semilattice of archimedean
components each of which contains at most one idempotemt. The components of a compact commutative semigroup need not be compact
(nor Γ-compact) as the congruence providing the decomposition is not necessarily closed. However, any component with CEP which
is Γ-compact is characterized by the afore-mentioned result. Characterization of components of a compact commutative semigroup
having CEP is a natural step towar characterization of the entire semigroup since CEP is a hereditary property. Other results
prevented in this paper give a characterization of compact monothetic semigroups with CEP and show that Rees quotients of
compact semigroups with CEP retain CEP. 相似文献
4.
Jing Wang 《Semigroup Forum》2007,75(2):388-392
We consider a congruence ρ on a semigroup S as a subsemigroup of the direct product S × S. We prove that if ρ has finite derivation
type (FDT), then so does S. 相似文献
5.
Xilin Tang 《代数通讯》2013,41(11):5439-5461
6.
P. M. Edwards 《Semigroup Forum》1989,39(1):257-262
For a congruence σ on a semigroupS a congruence μ(σ) onS, containing σ, is defined such that the semigroupS/σ is fundamental if and only if σ=μ(σ). The congruence μ(σ) is shown to possess maximality properties and for idempotent-surjective
semigroups, μ(σ) is the maximum congruence with respect to the partition of the idempotents determined by σ. Thus μ is the
maximum idempotent-separating congruence on any idempotent-surjective semigroup. It is shown that μ(μ(σ))=μ(σ).
If ρ is another congruence onS, possibly with the same partition of the idempotents as σ, then it is of interest to know when ρ⊆σ (or ρ⊆μ(σ)) implies μ(ρ)⊆μ(σ)
or even μ(ρ)=μ(σ). These implications are not true in general but if σ⊆ρ⊆μ(σ) then μ(ρ)⊆μ(σ). IfS is an idempotent-surjective semigroup and ρ and σ have the same partition of the idempotents then μ(ρ)=μ(σ). 相似文献
7.
Xianzhong Zhao 《Semigroup Forum》2002,64(2):289-296
For every semigroup S , we define a congruence relation ρ on the power semiring (P(S),\cup,\circ) of S . If S is a band, then P(S)/ρ is an idempotent semiring . This enables us to find models for the free objects in the variety of idempotent semiring s
whose additive reduct is a semilattice.
December 28, 1999 相似文献
8.
In this paper we define the radical ϱ
k
(k∈Z
+) of a relation ϱ on an arbitrary semigroup. Also, we define various types of k-regularity of semigroups and various types of k-Archimedness of semigroups. Using these notions we describe the structure of semigroups in which ρ
k
is a band (semilattice) congruence for some Green’s relation. 相似文献
9.
Let S be a regular semigroup with an inverse transversal S° and C(S) the congruence lattice of S. A relation K° on C(S) is introduced as follows: if ρ, θ∈ C(S), then we say that ρ and θ are K°-related if Ker ρ° = Ker θ° , where ρ° = ρ|S°. Expressions for the least and the greatest congruences in the same K°-class as ρ are provided. A number of equivalent conditions for K° being a congruence are given. 相似文献
10.
11.
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 using 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. 相似文献
12.
An ordered semigroup S is called CS-indecomposable if the set S × S is the only complete semilattice congruence on S. In the
present paper we prove that each ordered semigroup is, uniquely, a complete semilattice of CS-indecomposable semigroups, which
means that it can be decomposed into CS-indecomposable components in a unique way. Furthermore, the CS-indecomposable ordered
semigroups are exactly the ordered semigroups that do not contain proper filters. Bibliography: 6 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 343, 2007, pp. 222–232. 相似文献
13.
Norman R. Reilly 《Semigroup Forum》1973,6(1):153-170
Gluskin [2] has shown that if α is an isomorphism of a weakly reductive semigroup S onto a semigroup T, if V is a dense extension
of S and T is densely embedded in W then α extends uniquely to an isomorphism of V into W. Here we consider the problem of
extending epimorphisms and as a consequence of a few simple observations obtain as the main theorem a homomorphism of Ω(S),
for any semisimple semigroup S, into the product of the translational hulls of the principal factors of S. A few consequences
are considered. 相似文献
14.
Klaus Keimel 《Semigroup Forum》1971,2(1):55-63
Let R be a commutative semigroup [resp. ring] with identity and zero, but without nilpotent elements. We say that R is a Stone
semigroup [Baer ring], if for each annihilator ideal P⊂R there are idempotents e1 ε P and e2 ε Ann(P) such that x→(e1x, e2x):R→P×Ann(P) is an isomorphism. We show that for a given R there exists a Stone semigroup [Baer ring] S containing R that
is minimal with respect to this property. In the ring case, S is uniquely determined if one requires that there be a natural
bijection between the sets of annihilator ideals of R and S. This is close to results of J. Kist [5]. Like Kist, we use elementary
sheaf-theoretical methods (see [2], [3], [6]). Proofs are not very detailed.
An address delivered at the Symposium on Semigroups and the Multiplicative Structure of Rings, University of Puerto Rico,
Mayaguez, Puerto Rico, March 9–13, 1970. 相似文献
15.
V. D. Derech 《Ukrainian Mathematical Journal》2012,63(9):1390-1399
For a semigroup S, the set of all isomorphisms between the subsemigroups of the semigroup S with respect to composition is an inverse monoid denoted by PA(S) and called the monoid of local automorphisms of the semigroup S. The semigroup S is called permutable if, for any couple of congruences ρ and σ on S, we have ρ ∘ σ = σ ∘ ρ. We describe the structures of a finite commutative inverse semigroup and a finite bundle whose monoids of local automorphisms
are permutable. 相似文献
16.
Certain congruences on E-inversive E-semigroups 总被引:10,自引:0,他引:10
A semigroup S is called E-inversive if for every a ∈ S there exists x ∈ S such that ax is idempotent. S is called E-semigroup if the set of idempotents of S forms a subsemigroup. In this paper some special congruences on E-inversive E-semigroups are investigated, such as the least
group congruence, a certain semilattice congruence, some regular congruences and a certain idempotent-separating congruence. 相似文献
17.
Christian LeMerdy 《Semigroup Forum》1998,56(2):205-224
t )t≥0 on a Hilbert space H, we establish conditions under which (Tt)t≥0 is similar to a contraction semigroup, i.e., there exists an isomorphism S Ε B (H) such that (S-1 Tt S)t≥0 is a contraction semigroup. In the case when the generator -A of (Tt)t≥0 is one-to-one, we obtain that (Tt)t≥0 is similar to a contraction semigroup if and only if A admits bounded imaginary powers. This characterizes one-to-one operators
of type strictly less than π/2 on H which belong to BIP (H). 相似文献
18.
The purpose of this paper is to examine the structure of those semigroups which satisfy one or both of the following conditions:
Ar(Aℓ): The Rees right (left) congruence associated with any right (left) ideal is a congruence.
The conditions Ar and Aℓ are generalizations of commutativity for semigroups. This paper is a continuation of the work of Oehmke [5] and Jordan [4]
on H-semigroups (H for hamiltonian, a semigroup is called an H-semigroup if every one-sided congruence is a two-sided congruence).
In fact the results of section 2 of Oehmke [5] are proved here under the condition Ar and/or Aℓ and not the stronger hamiltonian condition.
Section 1 of this paper is essentially a summary of the known results of Oehmke. In section 2 we examine the structure of
irreducible semigroups satisfying the condition Ar and/or Aℓ. In particular we determine all regular (torsion) irreducible semigroups satisfying both the conditions Ar and Aℓ.
This research has been supported by Grant A7877 of the National Research Council of Canada. 相似文献
19.
We consider a congruence on a semigroup S as a subsemigroup of the
direct product S × S. Then we prove that if is finitely
presented then both S and S/ are finitely presented. 相似文献
20.
In the present paper, it is shown that a left cancellative
semigroup S (not necessarily with identity) is left amenable
whenever the Banach algebra ℓ1(S) is approximately amenable. It is also proved that if S is a Brandt semigroup over a group
G with an index set I, then ℓ1(S) is approximately
amenable if and only if G is amenable. Moreover ℓ1(S) is amenable if and only if G is amenable and I is finite. For a
left cancellative foundation semigroup S with an identity such
that for every Ma(S)-measurable subset B of S
and s ∈ S the set sB is Ma(S)-measurable,
it is proved that if the measure algebra Ma(S) is approximately
amenable, then S is left amenable. Concrete examples are given
to show that the converse is negative. 相似文献