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1.
Let S be a grading monoid with quotient group q(S) , let F(S) be the set of fractional ideals of S . For A ∈ F(S) , define A
w
= {x ∈ q(S) \mid J+x \subseteq A for some f.g. ideal J of S with J
-1
=S} and A_ \overline w ={x ∈ q(S)\mid J+x \subseteq A for some ideal J of S with J
-1
=S} . Then w and \overline w are star-operations on F(S) such that w ≤ \overline w . Using these star-operations, we give characterizations of Krull semigroups and pre-Krull semigroups. Also we show that
for every maximal * -ideal P of S , if S
P
is a valuation semigroup, then * -cancellation ideals are * -locally principal ideals, where * is a star-operation on S of finite character. Finally, we show that S is a pre-Krull semigroup (H-semigroup) if and only if the polynomial semigroup S[x] is a pre-Krull semigroup (H-semigroup).
October 15, 1999 相似文献
2.
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
3.
Let S =∪(Gα : α ∈ E) be a semilattice of groups(i.e., a Cliford semigroup) and n a natural number. E is called an n-element chain of groups if it is an n-element chain. Denote by Cn the set of all n-element chains of groups. In this paper we shall show that for any natural number n, the class of semigroups Cn satisfies the strong isomorphism property. 相似文献
4.
R. Exel 《Semigroup Forum》2009,79(1):159-182
By a Boolean inverse semigroup we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse
semigroup
in a Boolean inverse semigroup which are tight in a certain well defined technical sense. These representations are supposed to preserve as much as possible any trace of
Booleanness present in the semilattice of idempotents of
. After observing that the Vagner–Preston representation is not tight, we exhibit a canonical tight representation for any
inverse semigroup with zero, called the regular tight representation. We then tackle the question as to whether this representation is faithful, but it turns out that the answer is often negative.
The lack of faithfulness is however completely understood as long as we restrict to continuous inverse semigroups, a class generalizing the E
*-unitaries.
Partially supported by CNPq. 相似文献
5.
L. Olsen 《Monatshefte für Mathematik》2008,155(2):191-203
In this paper we consider the relationship between the topological dimension
and the lower and upper q-Rényi dimensions
and
of a Polish space X for q ∈ [1, ∞]. Let
and
denote the Hausdorff dimension and the packing dimension, respectively. We prove that
for all analytic metric spaces X (whose upper box dimension is finite) and all q ∈ (1, ∞); of course, trivially,
for all q ∈ [1, ∞]. As a corollary to this we obtain the following result relating the topological dimension and the lower and upper
q-Rényi dimensions:
for all Polish spaces X and all q ∈ [1, ∞]; in (1) and (2) we have used the following notation, namely, for two metric spaces X and Y, we write X ∼ Y if and only if X is homeomorphic to Y. Equality (1) has recently been proved for q = ∞ by Myjak et al.
Author’s address: Department of Mathematics, University of St. Andrews, St. Andrews, Fife KY16 9SS, Scotland 相似文献
6.
M. Zubor 《Acta Mathematica Hungarica》2016,150(2):512-523
We show that if Y is a subsemilattice of a finite semilattice indecomposable semigroup S then \({|Y|\leq 2\left\lfloor \frac{|S|-1}{4}\right\rfloor+1}\). We also characterize finite semilattice indecomposable semigroups S which contain a subsemilattice Y with \({|S|=4k+1}\) and \({|Y|=2\left\lfloor \frac{|S|-1}{4} \right\rfloor+1=2k+1}\). They are special inverse semigroups. Our investigation is based on our new result proved in this paper which characterizes finite semilattice indecomposable semigroups with a zero by using only the properties of its semigroup algebra. 相似文献
7.
Xilin Tang 《Semigroup Forum》1998,56(2):228-264
ρT on a semigroup of T of S extends to the semigroup S, if there exists a congruence ρ on s such that ρ|T= ρT. A semigroup S has the congruence extension property, CEP, if each congruence on each semigroup extends to S. In this paper
we characterize the semigroups with CEP by a set of conditions on their structure (by this we answer a problem put forward
in [1]). In particular, every such semigroup is a semilattice of nil extensions of rectangular groups. 相似文献
8.
For a large class of locally compact semitopological semigroups S, the Stone-Čech compactification β
S is a semigroup compactification if and only if S is either discrete or countably compact. Furthermore, for this class of semigroups which are neither discrete nor countably
compact, the quotient
contains a linear isometric copy of ℓ
∞. These results improve theorems by Baker and Butcher and by Dzinotyiweyi. 相似文献
9.
A. Malheiro 《Semigroup Forum》2012,84(3):515-526
In this paper we investigate how the combinatorial property finite derivation type (FDT) is preserved in a semilattice of semigroups. We prove that if $S= \mathcal{S}[Y,S_{\alpha}]$ is a semilattice of semigroups such that Y is finite and each S ?? (????Y) has FDT, then S has FDT. As a consequence we can show that a strong semilattice of semigroups $\mathcal{S}[Y,S_{\alpha},\lambda_{\alpha,\beta}]$ has FDT if and only if Y is finite and every semigroup S ?? (????Y) has FDT. 相似文献
10.
Liu Chuan ZENG 《数学学报(英文版)》2006,22(2):407-416
Let G be a semitopological semigroup. Let C be a closed convex subset of a uniformly convex Banaeh space E with a Frechet differentiable norm, and T = {Tt : t ∈ G} be a continuous representation of G as nearly asymptotically nonexpansive type mappings of C into itself such that the common fixed point set F(T) of T in C is nonempty. It is shown that if G is right reversible, then for each almost-orbit u(.) of T, ∩s∈G ^-CO{u(t) : t ≥ s} ∩ F(T) consists of at most one point. Furthermore, ∩s∈G ^-CO{Ttx : t ≥ s} ∩ F(T) is nonempty for each x ∈ C if and only if there exists a nonlinear ergodic retraction P of C onto F(T) such that PTs - TsP = P for all s ∈ G and Px ∈^-CO{Ttx : s ∈ G} for each x ∈ C. This result is applied to study the problem of weak convergence of the net {u(t) : t ∈ G} to a common fixed point of T. 相似文献
11.
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
12.
13.
Alex Zhai 《Semigroup Forum》2013,86(3):634-662
We give an asymptotic estimate of the number of numerical semigroups of a given genus. In particular, if n g is the number of numerical semigroups of genus g, we prove that $$\lim_{g \rightarrow \infty} n_g \varphi^{-g} = S $$ where $\varphi = \frac{1 + \sqrt{5}}{2}$ is the golden ratio and S is a constant, resolving several related conjectures concerning the growth of n g . In addition, we show that the proportion of numerical semigroups of genus g satisfying f<3m approaches 1 as g→∞, where m is the multiplicity and f is the Frobenius number. 相似文献
14.
In this paper, we give a direct proof that every strongly
inverse semigroup can be embedded into a 0-semidirect product of a semilattice with zero by a group. As a corollary, we obtain a new proof of the structure theory of strongly
inverse semigroups described in [1]. We also prove that the strongly
inverse semigroups are precisely
inverse semigroups equipped with a
, idempotent pure prehomomorphism to a primitive inverse semigroup. 相似文献
15.
For fixed generalized reflection matrix P, i.e. P
T
= P, P
2 = I, then matrix X is said to be generalized bisymmetric, if X = X
T
= PXP. In this paper, an iterative method is constructed to find the generalized bisymmetric solutions of the matrix equation A
1
X
1
B
1 + A
2
X
2
B
2 + ⋯ + A
l
X
l
B
l
= C where [X
1,X
2, ⋯ ,X
l
] is real matrices group. By this iterative method, the solvability of the matrix equation can be judged automatically. When
the matrix equation is consistent, for any initial generalized bisymmetric matrix group , a generalized bisymmetric solution group can be obtained within finite iteration steps in the absence of roundoff errors,
and the least norm generalized bisymmetric solution group can be obtained by choosing a special kind of initial generalized
bisymmetric matrix group. In addition, the optimal approximation generalized bisymmetric solution group to a given generalized
bisymmetric matrix group in Frobenius norm can be obtained by finding the least norm generalized bisymmetric solution group of the new matrix equation
, where . Given numerical examples show that the algorithm is efficient.
Research supported by: (1) the National Natural Science Foundation of China (10571047) and (10771058), (2) Natural Science
Foundation of Hunan Province (06JJ2053), (3) Scientific Research Fund of Hunan Provincial Education Department(06A017). 相似文献
16.
The Weiss conjecture on admissibility of observation operators for contraction semigroups 总被引:4,自引:0,他引:4
We prove the conjecture of George Weiss for contraction semigroups on Hilbert spaces, giving a characterization of infinite-time admissible observation functionals for a contraction semigroup, namely that such a functionalC is infinite-time admissible if and only if there is anM>0 such that
for alls in the open right half-plane. HereA denotes the infinitesimal generator of the semigroup. The result provides a simultaneous generalization of several celebrated results from the theory of Hardy spaces involving Carleson measures and Hankel operators. 相似文献
17.
Let Y be a subset of X and T(X, Y) the set of all functions from X into Y. Then, under the operation of composition, T(X, Y) is a subsemigroup of the full transformation semigroup T(X). Let E be an equivalence on X. Define a subsemigroup $$T_E(X,Y)$$ of T(X, Y) by $$\begin{aligned} T_E(X,Y)=\{\alpha \in T(X,Y):\forall (x,y)\in E, (x\alpha ,y\alpha )\in E\}. \end{aligned}$$Then $$T_E(X,Y)$$ is the semigroup of all continuous self-maps of the topological space X for which all E-classes form a basis carrying X into a subspace Y. In this paper, we give a necessary and sufficient condition for $$T_E(X,Y)$$ to be regular and characterize Green’s relations on $$T_E(X,Y)$$. Our work extends previous results found in the literature. 相似文献
18.
Given H≥0 and bounded convex curves α1, ...,⇌n, α in the plane z=0 bounding domains D1, …, Dn, D, respectively, with
if i ∈ j and with Di ⊂ D, we obtain several results proving the existence of a constanth depending only on H and on the geometry of the curves
αi, α such that the Dirichlet problem for the constant mean curvature H equation:
where
may accept or not a solution. 相似文献
19.
It has been known since the 1970s that the Torelli map M
g
→A
g
, associating to a smooth curve its Jacobian, extends to a regular map from the Deligne–Mumford compactification
[`(\operatorname M)]g\overline {\operatorname {M}}_{g} to the 2nd Voronoi compactification
[`(\operatorname A)]gvor\overline {\operatorname {A}}_{g}^{\mathrm {vor}}. We prove that the extended Torelli map to the perfect cone (1st Voronoi) compactification
[`(\operatorname A)]gperf\overline {\operatorname {A}}_{g}^{\mathrm {perf}} is also regular, and moreover
[`(\operatorname A)]gvor\overline {\operatorname {A}}_{g}^{\mathrm {vor}} and
[`(\operatorname A)]gperf\overline {\operatorname {A}}_{g}^{\mathrm {perf}} share a common Zariski open neighborhood of the image of
[`(\operatorname M)]g\overline {\operatorname {M}}_{g}. We also show that the map to the Igusa monoidal transform (central cone compactification) is not regular for g≥9; this disproves a 1973 conjecture of Namikawa. 相似文献
20.
Just as complete lattices can be viewed as the completions of posets, quantales can also be treated as the completions of partially ordered semigroups. Motivated by the study on the well-known Frink completions of posets, it is natural to consider the “Frink” completions for the case of partially ordered semigroups. For this purpose, we firstly introduce the notion of precoherent quantale completions of partially ordered semigroups, and construct the concrete forms of three types of precoherent quantale completions of a partially ordered semigroup. Moreover, we obtain a sufficient and necessary condition of the Frink completion on a partially ordered semigroup being a precoherent quantale completion. Finally, we investigate the injectivity in the category $$\mathbf {APoSgr}_{\le }$$ of algebraic partially ordered semigroups and their submultiplicative directed-supremum-preserving maps, and show that the $$\mathscr {E}_{\le }$$-injective objects of algebraic partially ordered semigroups are precisely the precoherent quantales, here $$\mathscr {E}_{\le }$$ denote the class of morphisms $$h:A\longrightarrow B$$ that preserve the compact elements and satisfy that $$h(a_1)\cdots h(a_n)\le h(b)$$ always implies $$a_1\cdots a_n\le b$$. 相似文献