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1.
Recep Korkmaz 《Semigroup Forum》2009,78(3):528-535
In this paper we study dense inverse subsemigroups of topological inverse semigroups. We construct a topological inverse semigroup
from a semilattice. Finally, we give two examples of the closure of B
( −∞, ∞ )1, a topological inverse semigroup obtained by starting with the real numbers as a semilattice with the operation a
∨
b=sup{a,b}.
The author would like to thank to the referee for useful suggestions. 相似文献
2.
By an associate inverse subsemigroup of a regular semigroup S we mean a subsemigroup T of S containing a least associate of each x∈S, in relation to the natural partial order ≤
S
. We describe the structure of a regular semigroup with an associate inverse subsemigroup, satisfying two natural conditions.
As a particular application, we obtain the structure of regular semigroups with an associate subgroup with medial identity
element.
Research supported by the Portuguese Foundation for Science and Technology (FCT) through the research program POCTI. 相似文献
3.
Amal AlAli 《代数通讯》2017,45(11):4667-4678
4.
A semigroup S is called a Clifford semigroup if it is completely regular and inverse. In this paper, some relations related to the least
Clifford semigroup congruences on completely regular semigroups are characterized. We give the relation between Y and ξ on completely regular semigroups and get that Y
* is contained in the least Clifford congruence on completely regular semigroups generally. Further, we consider the relation
Y
*, Y, ν and ε on completely simple semigroups and completely regular semigroups.
This work is supported by Leading Academic Discipline Project of Shanghai Normal University, Project Number: DZL803 and General
Scientific Research Project of Shanghai Normal University, No. SK200707. 相似文献
5.
Donald B. McAlister 《代数通讯》2013,41(6):2002-2023
6.
Nick Dungey 《Semigroup Forum》2009,78(2):226-237
For suitable bounded operator semigroups (e
tA
)
t≥0 in a Banach space, we characterize the estimate ‖Ae
tA
‖≤c/F(t) for large t, where F is a function satisfying a sublinear growth condition. The characterizations are by holomorphy estimates on the semigroup,
and by estimates on powers of the resolvent. We give similar characterizations of the difference estimate ‖T
n
−T
n+1‖≤c/F(n) for a power-bounded linear operator T, when F(n) grows faster than n
1/2 for large n. 相似文献
7.
Let
be a dense sub-semigroup of ℝ+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of
operators on X over
can be extended to a weakly continuous semigroup over ℝ+. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized
semigroups which are extendable to semigroups over ℝ+.
O.M. Shalit was partially supported by the Gutwirth Fellowship. 相似文献
8.
Let S° be an inverse semigroup with semilattice biordered set E° of idempotents and E a weakly inverse biordered set with a subsemilattice Ep = { e ∈ E | arbieary f ∈ E, S(f , e) loheain in w(e)} isomorphic to E° by θ:Ep→E°. In this paper, it is proved that if arbieary f, g ∈E, f ←→ g→→ f°θD^s° g°θand there exists a mapping φ from Ep into the symmetric weakly inverse semigroup P J(E∪ S°) satisfying six appropriate conditions, then a weakly inverse semigroup ∑ can be constructed in P J(S°), called the weakly inverse hull of a weakly inverse system (S°, E, θ, φ) with I(∑) ≌ S°, E(∑) ∽- E. Conversely, every weakly inverse semigroup can be constructed in this way. Furthermore, a sufficient and necessary condition for two weakly inverse hulls to be isomorphic is also given. 相似文献
9.
Given a subgroup G of the symmetric group S
n
on n letters, a semigroup S of transformations of X
n
is G-normal if G
S
=G, where G
S
consists of all permutations h∈S
n
such that h
−1
fh∈S for all f∈S. A semigroup S is G-normax if it is a maximal semigroup in the set of all G-normal semigroups.
In 1996, I. Levi showed that the alternating group A
n
can not serve as the group G
S
for any semigroup of total transformations of X
n
. In 2000 and 2001, I. Levi, D.B. McAlister and R.B. McFadden described all A
n
-normal semigroups of partial transformations of X
n
. Also, in 1994, I. Levi and R.B. McFadden described all S
n
-normal semigroups.
In this paper, we show that the dihedral group D
n
may serve as the group G
S
for semigroups of transformations of X
n
. We characterize a large class of D
n
-normax semigroups and describe certain D
n
-normal semigroups. 相似文献
10.
Zhenji Tian 《代数通讯》2013,41(6):1824-1833
An inverse semigroup S is said to be 0-semidistributive if its lattice ?F (S) of full inverse subsemigroups is 0-semidistributive. We show that it is sufficient to study simple inverse semigroups which are not groups. Our main theorem states that such a simple inverse semigroup S is 0-semidistributive if and only if (1) S is E-unitary, (2) S is aperiodic, (3) for any a,b ∈ S/σ with ab ≠ 1, there exist nonzero integers n and m such that (ab) m = a n or (ab) m = b n , where σ is the minimum group congruence on S. 相似文献
11.
本文研究了N(2,2,0)代数(S,*,△,0)的E-反演半群.利用N(2,2,0)代数的幂等元,弱逆元,中间单位元的性质和同宇关系,得到了N(2,2,0)代数的半群(S,*)构成E-反演半群的条件及元素α的右伴随非零零因子唯一,且为α的弱逆元等结论,这些结果进一步刻画了N(2,2,0)代数的结构. 相似文献
12.
Recall that the semigroups S and R are said to be strongly Morita equivalent if there exists a unitary Morita context (S, R.,
S
P
R,R
Q
S
,〈〉
, ⌈⌉) with 〈〉 and ⌈⌉ surjective. For a factorisable semigroup S, we denote ζ
S
= {(s
1, s
2) ∈S×S|ss
1 = ss
2, ∀s∈S}, S' = S/ζ
S
and US-FAct = {
S
M∈S− Act |SM = M and SHom
S
(S, M) ≅M}. We show that, for factorisable semigroups S and M, the categories US-FAct and UR-FAct are equivalent if and only if the semigroups S' and R' are strongly Morita equivalent. Some conditions for a factorisable semigroups to be strongly Morita equivalent to a sandwich
semigroup, local units semigroup, monoid and group separately are also given. Moreover, we show that a semigroup S is completely simple if and only if S is strongly Morita equivalent to a group and for any index set I, S⊗SHom
S
(S, ∐
i∈I
S) →∐
i∈I
S, s⊗t·ƒ↦ (st)ƒ is an S-isomorphism.
The research is partially supported by a UGC(HK) grant #2160092.
Project is supported by the National Natural Science Foundation of China 相似文献
13.
Let I be an interval of positive rational numbers. Then the set S (I) = T ∩ N, where T is the submonoid of (Q0+, +) generated by T, is a numerical semigroup. These numerical semigroups are called proportionally modular and can be characterized as the set of integer solutions of a Diophantine inequality of the form ax rood b 〈 cx. In this paper we are interested in the study of the maximal intervals I subject to the condition that S (I) has a given multiplicity. We also characterize the numerical semigroups associated with these maximal intervals. 相似文献
14.
For any finite commutative idempotent semigroup S, a semilattice, we show how to compute the amenability constant of its semigroup algebra ℓ
1(S). This amenability constant is always of the form 4n+1. We then show that these give lower bounds to amenability constants of certain Banach algebras graded over semilattices.
We also give example of a commutative Clifford semigroups G
n
whose semigroup algebras ℓ
1(G
n
) admit amenability constants of the form 41+4(n−1)/n. We also show there is no commutative semigroup whose semigroup algebra has an amenability constant between 5 and 9.
N. Spronk’s research was supported by NSERC Grant 312515-05. 相似文献
15.
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.
This work was supported by National Natural Science Foundation of China (Grant No. 10671151) and Natural Science Foundation
of Shaanxi Province (Grant No. SJ08A06), and partially by UGC (HK) (Grant No. 2160123) 相似文献
16.
The p
n
-sequence of a semigroup S is said to be polynomially bounded, if there exist a positive constant c and a positive integer r such that the inequality p
n
(S) ≤cn
r
holds for all n≥ 1. In this paper, we fully describe all finite semigroups having polynomially bounded p
n
-sequences. First we give a characterization in terms of identities satisfied by these semigroups. In the sequel, this result
will allow an insight into the structure of such semigroups. We are going to deal with certain ideals and the construction
of ideal extension of semigroups. In addition, we supply an effective procedure for deciding whether a finite semigroup has
polynomially bounded p
n
-sequence and give some examples.
Received March 5, 1999; accepted in final form November 1, 1999. 相似文献
17.
It is known that the bicyclic semigroup S
1 is an amenable inverse semigroup. In this note we show that the convolution semigroup algebra ℓ
1(S
1) is not approximately amenable. 相似文献
18.
In this article, we study commutative zero-divisor semigroups determined by graphs. We prove that for all n ≥ 4, the complete graph K n together with two end vertices has a unique corresponding zero-divisor semigroup, while the complete graph K n together with three end vertices has no corresponding semigroups. We determine all the twenty zero-divisor semigroups whose zero-divisor graphs are the complete graph K 3 together with an end vertex. 相似文献
19.
Bálint Farkas 《Czechoslovak Mathematical Journal》2011,61(2):309-322
For a given bi-continuous semigroup (T(t))
t⩾0 on a Banach space X we define its adjoint on an appropriate closed subspace X° of the norm dual X′. Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology σ(X°,X). We give the following application: For Ω a Polish space we consider operator semigroups on the space Cb(Ω) of bounded, continuous functions (endowed with the compact-open topology) and on the space M(Ω) of bounded Baire measures
(endowed with the weak*-topology). We show that bi-continuous semigroups on M(Ω) are precisely those that are adjoints of
bi-continuous semigroups on Cb(Ω). We also prove that the class of bi-continuous semigroups on Cb(ω) with respect to the compact-open topology coincides with the class of equicontinuous semigroups with respect to the strict
topology. In general, if is not a Polish space this is not the case. 相似文献
20.
Gerd Rodé 《Semigroup Forum》1983,26(1):317-321
It is proved that each continuous semigroup {P(t)}t≥0 of convex operators P(t):Rn→Rn is continuously differentiable with respect to t.
This note represents a first step towards a better understanding of semigroups formed by convex operators. We establish the
differentiability of a convex semigroup in the finite dimensional case, generalizing a basic result from linear semigroup
theory.
Our motivation for the study of semigroups of convex operators comes from the theory of Markov decision processes. In [1]
and in [2] it was shown that the maximum reward of these processes can be described by a certain nonlinear semigroup. The
nonlinear operators are defined as suprema of linear operators (plus a constant), hence they are convex operators.
It seems that the convexity assumption keeps its smoothing influence even in the infinite dimensional situation. We hope to
discuss this in a future paper. 相似文献