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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.
Ján Jakubík 《Czechoslovak Mathematical Journal》2007,57(1):243-252
The notion of idempotent modification of an algebra was introduced by Ježek. He proved that the idempotent modification of
a group is subdirectly irreducible. For an MV-algebra
we denote by
, A and
the idempotent modification, the underlying set or the underlying lattice of
, respectively. In the present paper we prove that if
is semisimple and
is a chain, then
is subdirectly irreducible. We deal also with a question of Ježek concerning varieties of algebras. 相似文献
3.
Ján Jakubík 《Czechoslovak Mathematical Journal》2007,57(1):161-171
In this paper we investigate the relations between isometries and direct product decompositions of generalized MV-algebras. 相似文献
4.
Ján Jakubík 《Czechoslovak Mathematical Journal》2007,57(4):1099-1105
A generalized MV-algebra A is called representable if it is a subdirect product of linearly ordered generalized MV-algebras. Let S be the system of all congruence relations ϱ on A such that the quotient algebra A/ϱ is representable. In the present paper we prove that the system S has a least element.
This work was supported by Science and Technology Assistance Agency under Contract No AVPT-51-032002.
The 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
5.
Ján Jakubík 《Czechoslovak Mathematical Journal》2008,58(1):183-202
In the present paper we deal with generalized MV-algebras (GMV-algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, GMV-algebras can be obtained by a truncation construction from lattice ordered groups. We investigate direct summands and retract
mappings of GMV-algebras. The relations between GMV-algebras and lattice ordered groups are essential for this investigation.
Supported by VEGA Agency grant 1/2002/05.
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
6.
For a big number of varieties
of groups close to Engelian, it is proved that a variety of lattice-ordered groups generated by all linearly ordered groups
in the class
does not coincide with the variety
of all o-approximable lattice-ordered groups.
Supported by FP “Universities of Russia” grant No. UR.04.01.001.
__________
Translated from Algebra i Logika, Vol. 45, No. 1, pp. 20–27, January–February, 2006. 相似文献
7.
Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single
individual variable occurs. GMV-algebras are a non-commutative generalization of MV-algebras and are an algebraic counterpart of the non-commutative Łukasiewicz infinite valued logic. We introduce monadic
GMV-algebras and describe their connections to certain couples of GMV-algebras and to left adjoint mappings of canonical embeddings of GMV-algebras. Furthermore, functional MGMV-algebras are studied and polyadic GMV-algebras are introduced and discussed.
The first author was supported by the Council of Czech Government, MSM 6198959214. 相似文献
8.
Elmiloud Chil 《Positivity》2004,8(3):257-267
It is shown that the multiplication in an Archimedean d-algebra A can be extended to a multiplication in the Dedekind completion A
of A such that A
becomes a d-algebra with respect to this extended multiplication. This answers a question posed by Huijsmans in Studies in Economic Theory (Vol. 2, Springer, Berlin, 1991). 相似文献
9.
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
10.
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
11.
YiChuan Yang 《中国科学A辑(英文版)》2009,52(11):2397-2403
Let A be a lattice-ordered group. Gusi′c showed that A can be equipped with a C-topology which makes A into a topological group. We give a generalization of Gusi′c's theorem,and reveal the very nature of a "C-group" of Gusi′c in this paper. Moreover,we show that the C-topological groups are topological lattice-ordered groups,and prove that every archimedean lattice-ordered vector space is a T2 topological lattice-ordered vector space under the C-topology. An easy example shows that a C-group need not be T2.... 相似文献
12.
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
13.
Let be a field of characteristic and S
1 the unit circle. We prove that the shc-structure on a cochain algebra (A,d
A
) induces an associative product on the negative cyclic homology HC
*−
A. When the cochain algebra (A,d
A
) is the algebra of normalized cochains of the simply connected topological space X with coefficients in , then HC
*−
A is isomorphic as a graded algebra to the S
1-equivariant cohomology algebra of LX, the free loop space of X. We use the notion of shc-formality introduced in Topology 41, 85–106 (2002) to compute the S
1-equivariant cohomology algebras of the free loop space of the complex projective space when n + 1 = 0 [p] and of the even spheres S
2n
when p = 2.
相似文献
14.
Ján Jakubík 《Mathematica Slovaca》2010,60(2):179-188
The notion of idempotent modification of an algebra was introduced by Je?ek; he proved that the idempotent modification of a group is always subdirectly irreducible. In the present note we show that the idempotent modification of a generalized MV -algebra having more than two elements is directly irreducible if and only if there exists an element in A which fails to be boolean. Some further results on idempotent modifications are also proved. 相似文献
15.
16.
Choonkil PARK Jian Lian CUI 《数学学报(英文版)》2007,23(11):1919-1936
Let X and Y be vector spaces. The authors show that a mapping f : X →Y satisfies the functional equation 2d f(∑^2d j=1(-1)^j+1xj/2d)=∑^2dj=1(-1)^j+1f(xj) with f(0) = 0 if and only if the mapping f : X→ Y is Cauchy additive, and prove the stability of the functional equation (≠) in Banach modules over a unital C^*-algebra, and in Poisson Banach modules over a unital Poisson C*-algebra. Let A and B be unital C^*-algebras, Poisson C^*-algebras or Poisson JC^*- algebras. As an application, the authors show that every almost homomorphism h : A →B of A into is a homomorphism when h((2d-1)^nuy) =- h((2d-1)^nu)h(y) or h((2d-1)^nuoy) = h((2d-1)^nu)oh(y) for all unitaries u ∈A, all y ∈ A, n = 0, 1, 2,....
Moreover, the authors prove the stability of homomorphisms in C^*-algebras, Poisson C^*-algebras or Poisson JC^*-algebras. 相似文献
17.
In this paper, we will discuss some properties of biprojection-commutative elements which are relevant to the classification
of certain infinite C*-algebras, and define an important invariant s(A) of C*-algebra A as well as give some basic properties with regard to s(A). Moreover we prove that the invariant s(A) has continuity. 相似文献
18.
Abdellah El Kinani 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):229-238
We endow any proper A-convex H*-algebra (E, τ) with a locally pre-C*-topology. The latter is equivalent to that introduced by the pre C*-norm given by Ptàk function when (E, τ) is a Q-algebra. We also prove that the algebra of complex numbers is the unique proper locally A-convex H*-algebra which is barrelled and Q-algebra.
相似文献
19.
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
20.
Let
be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are presented: (1) G ∈
if and only if there is a normal subgroup H such that G/H ∈
and every maximal subgroup of all Sylow subgroups of H is either c-normal or S-quasinormally embedded in G. (2) G ∈
if and only if there is a normal subgroup H such that G/H ∈
and every maximal subgroup of all Sylow subgroups of F*(H), the generalized Fitting subgroup of H, is either c-normal or S-quasinormally embedded in G. (3) G ∈
if and only if there is a normal subgroup H such that G/H ∈
and every cyclic subgroup of F*(H) of prime order or order 4 is either c-normal or S-quasinormally embedded in G.
Supported by the Natural Science Foundation of China and the Natural Science Foundation of Guangxi Autonomous Region (No.
0249001).
Corresponding author. Supported in part by the Natural Science Foundation of China (10571181), NSF of Guangdong Province (06023728)
and ARF(GDEI). 相似文献