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1.
Ján Jakubík 《Mathematica Slovaca》2008,58(2):143-154
For an MV-algebra
let J
0(
) be the system of all closed ideals of
; this system is partially ordered by the set-theoretical inclusion. A radical class X of MV-algebras will be called a K-radical class iff, whenever
∈ X and
is an MV-algebra with J
0(
) ≅ J
0(
), then
∈ X. An analogous notation for lattice ordered groups was introduced and studied by Conrad. In the present paper we show that
there is a one-to-one correspondence between K-radical classes of MV-algebras and K-radical classes of abelian lattice ordered groups. We also prove an analogous result for product radical classes of MV-algebras; product radical classes of lattice ordered groups were studied by Ton.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information,
Grant I/2/2005. 相似文献
2.
Jia Feng Lü 《数学学报(英文版)》2009,25(6):1015-1030
The so-called weakly d-Koszul-type module is introduced and it turns out that each weakly d-Koszul-type module contains a d-Koszul-type submodule. It is proved that, M ∈ W H J^d(A) if and only if M admits a filtration of submodules: 0 belong to U0 belong to U1 belong to ... belong to Up = M such that all Ui/Ui-1 are d-Koszul-type modules, from which we obtain that the finitistic dimension conjecture holds in W H J^d(A) in a special case. Let M ∈ W H J^d(A). It is proved that the Koszul dual E(M) is Noetherian, Hopfian, of finite dimension in special cases, and E(M) ∈ gr0(E(A)). In particular, we show that M ∈ W H J^d(A) if and only if E(G(M)) ∈ gr0(E(A)), where G is the associated graded functor. 相似文献
3.
In this paper we discuss the K-groups of Wiener algebra ;W. For the 1-shift space XGM2,We obtain a characterization of Fredholm operators on X^nGM2 for all n ∈ N. We also calculate the K-groups of operator algebra on the 1-shift space XGM2. 相似文献
4.
If X is a space that can be mapped onto a metric space by a one-to-one mapping, then X is said to have a weaker metric topology.
In this paper, we give characterizations of sequence-covering compact images and sequentially-quotient compact images of spaces
with a weaker metric topology. The main results are that
(1) Y is a sequence-covering compact image of a space with a weaker metric topology if and only if Y has a sequence
of point-finite cs-covers such that
for each y ∈ Y.
(2) Y is a sequentially-quotient compact image of a space with a weaker metric topology if and only if Y has a sequence
of point-finite cs*-covers such that
for each y ∈ Y.
Supported by the NNSF(10471084) of China. 相似文献
5.
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
6.
Lining Jiang 《Siberian Mathematical Journal》2009,50(2):360-367
Let be a C*-discrete quantum group and let be the discrete quantum group associated with . Suppose that there exists a continuous action of on a unital C*-algebra so that becomes a -algebra. If there is a faithful irreducible vacuum representation π of on a Hilbert space H = with a vacuum vector Ω, which gives rise to a -invariant state, then there is a unique C*-representation (θ, H) of supplemented by the action. The fixed point subspace of under the action of is exactly the commutant of θ().
相似文献
7.
Ján Jakubík 《Mathematica Slovaca》2008,58(5):521-534
A class of lattice ordered groups is called a formation if it is closed with respect to homomorphic images and finite subdirect
products. Analogously we define the formation of GMV-algebras. Let us denote by ℱ1 and ℱ2 the collection of all formations of lattice ordered groups or of GMV-algebras, respectively. Both ℱ1 and ℱ2 are partially ordered by the class-theoretical inclusion. We prove that ℱ1 satisfies the infinite distributivity law
and that ℱ2 is isomorphic to a principal ideal of ℱ1.
This work was supported by VEGA grant 2/7141/27. 相似文献
8.
In this paper we extend the notion of n-weak amenability of a Banach algebra
when n ∈ ℕ. Technical calculations show that when
is Arens regular or an ideal in
**, then
* is an
(2n)-module and this idea leads to a number of interesting results on Banach algebras. We then extend the concept of n-weak amenability to n ∈ ∕. 相似文献
9.
Long Miao 《Bulletin of the Brazilian Mathematical Society》2007,38(4):585-594
Let
be a class of groups. A subgroup H of a group G is called
-s-supplemented in G, if there exists a subgroup K of G such that G = HK and K/K ∩ HG belongs to
where HG is the maximal normal subgroup of G which is contained in H. The main purpose of this paper is to study some subgroups of Fitting subgroup and generalized Fitting subgroup
-s-supplemented and some new criterions of p-nilpotency of finite groups are obtained.
*This research is supported by the grant of NSFC and TianYuan Fund of Mathematics of China (Grant #10626047). 相似文献
10.
For C*-algebras A and B, the identity map from into A
λ
B is shown to be injective. Next, we deduce that the center of the completion of the tensor product A⊗B of two C*-algebras A and B with centers Z(A) and Z(B) under operator space projective norm is equal to . A characterization of isometric automorphisms of and A
h
B is also obtained.
Dedicated to Ajit Iqbal Singh on her 65th birthday. 相似文献
11.
Ján Jakubík 《Czechoslovak Mathematical Journal》2008,58(4):1129-1143
The notion of bounded commutative residuated ℓ-monoid (BCR ℓ-monoid, in short) generalizes both the notions of MV-algebra and of BL-algebra. Let
be a BCR ℓ-monoid; we denote by ℓ(
) the underlying lattice of
. In the present paper we show that each direct product decomposition of ℓ(
) determines a direct product decomposition of
. This yields that any two direct product decompositions of
have isomorphic refinements. We consider also the relations between direct product decompositions of
and states on
.
This work was supported by Slovak Research and Development Agency under the contract No APVV-0071-06.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information
(grant I/2/2005). 相似文献
12.
In this article we study the following Cauchy problem:
相似文献
13.
Ján Jakubík 《Czechoslovak Mathematical Journal》2009,59(1):183-196
In this paper we deal with a pseudo effect algebra
possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein,
can be represented as an interval of a unital partially ordered group G. We prove that
is projectable (strongly projectable) if and only if G is projectable (strongly projectable). An analogous result concerning weak homogeneity of
and of G is shown to be valid.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence—Physics of Information
(grant I/2/2005). 相似文献
14.
The degree conjecture for the Selberg class
of L-functions states that the degree d
F
of every F ∈
is an integer. Moreover, it is expected that every F ∈
has polynomial Euler product, and that the degree ∂
F
of such an Euler product coincides with d
F
. In this note we prove that a suitable continuity assumption on the degree d
F
implies that ∂
F
= d
F
for all F ∈
with polynomial Euler product.
相似文献
15.
Chun-Gil Park Hahng-Yun Chu Won-Gil Park Hee-Jeong Wee 《Czechoslovak Mathematical Journal》2005,55(4):1055-1065
It is shown that every almost linear Pexider mappings f, g, h from a unital C*-algebra
into a unital C*-algebra ℬ are homomorphisms when f(2
n
uy) = f(2
n
u)f(y), g(2
n
uy) = g(2
n
u)g(y) and h(2
n
uy) = h(2
n
u)h(y) hold for all unitaries u ∈
, all y ∈
, and all n ∈ ℤ, and that every almost linear continuous Pexider mappings f, g, h from a unital C*-algebra
of real rank zero into a unital C*-algebra ℬ are homomorphisms when f(2
n
uy) = f(2
n
u)f(y), g(2
n
uy) = g(2
n
u)g(y) and h(2
n
uy) = h(2
n
u)h(y) hold for all u ∈ {v ∈
: v = v* and v is invertible}, all y ∈
and all n ∈ ℤ.
Furthermore, we prove the Cauchy-Rassias stability of *-homomorphisms between unital C*-algebras, and ℂ-linear *-derivations on unital C*-algebras.
This work was supported by Korea Research Foundation Grant KRF-2003-042-C00008.
The second author was supported by the Brain Korea 21 Project in 2005. 相似文献
16.
We give a very simple and elementary proof of the existence of a weakly compact family of probability measures {Pθ : θ∈θ} representing an important sublinear expectation- G-expectation E[·]. We also give a concrete approximation of a bounded continuous function X(ω) by an increasing sequence of cylinder functions Lip(Ω) in order to prove that Cb(Ω) belongs to the completion of Lip(Ω) under the natural norm E[|·|]. 相似文献
17.
Given any R-semimodule M equipped with a semitopology
we construct an N-protosummation
for M. If
satisfies certain properties, then a similar construction leads to an unconditional N-summation
for M, that is an N-summation for M equipped with the trivial prenorm MD over the N-summation (DN,D) for D. Conversely any N-protosummation
on M gives rise to a topology
. If both
and
satisfy a certain separation property, then
and
form a Galois connection.
Dedicated to my friend and collegue Nico Pumplün on the occasion of his 70th birthdayMathematics Subject Classifications (2000) 16Y60, 54A05. 相似文献
18.
Ján Jakubík 《Mathematica Slovaca》2008,58(3):289-300
In a previous author’s paper, sequential convergences on an MV-algebra
have been studied; the Urysohn’s axiom was assumed to be valid. The system of all such convergences was denoted by Conv
. In the present paper we investigate analogous questions without supposing the validity of the Urysohn’s axiom; the corresponding
system of convergences is denoted by conv
. Both Conv
and conv
are partially ordered by the set-theoretical inclusion. We deal with the properties of conv 289-6 and the relations between conv
and Conv
. We prove that each interval of conv
is a distributive lattice. The system conv
has the least element, but it does not possess any atom. Hence it is either a singleton set or it is infinite. We consider
also the relations between conv
and conv G, where (G, u) is a unital lattice-ordered group with
= Γ (G, u).
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence — Physics of
Information, Grant 1/2/2005. 相似文献
19.
Yehuda Pinchover Kyril Tintarev 《Calculus of Variations and Partial Differential Equations》2007,28(2):179-201
Let Ω be a domain in , d ≥ 2, and 1 < p < ∞. Fix . Consider the functional Q and its Gateaux derivative Q′ given by If Q ≥ 0 on, then either there is a positive continuous function W such that for all, or there is a sequence and a function v > 0 satisfying Q′ (v) = 0, such that Q(u
k
) → 0, and in . In the latter case, v is (up to a multiplicative constant) the unique positive supersolution of the equation Q′ (u) = 0 in Ω, and one has for Q an inequality of Poincaré type: there exists a positive continuous function W such that for every satisfying there exists a constant C > 0 such that . As a consequence, we prove positivity properties for the quasilinear operator Q′ that are known to hold for general subcritical resp. critical second-order linear elliptic operators. 相似文献
20.
Let A be a compact set in of Hausdorff dimension d. For s ∈ (0,d) the Riesz s-equilibrium measure μ
s
is the unique Borel probability measure with support in A that minimizes
over all such probability measures. If A is strongly -rectifiable, then μ
s
converges in the weak-star topology to normalized d-dimensional Hausdorff measure restricted to A as s approaches d from below.
This research was supported, in part, by the U. S. National Science Foundation under grants DMS-0505756 and DMS-0808093. 相似文献