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1.
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
2.
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
3.
Filip Švrček 《Czechoslovak Mathematical Journal》2008,58(2):345-357
GMV-algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior
GMV-algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative
interior and additive closure operators on DRl-monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on GMV-algebras. 相似文献
4.
5.
Andrzej Walendziak 《Mathematica Slovaca》2007,57(2):119-128
In this paper we introduce the notion of BF-algebras, which is a generalization of B-algebras. We also introduce the notions of an ideal and a normal ideal in BF-algebras. We investigate the properties and characterizations of them.
相似文献
6.
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
7.
Bounded commutative residuated lattice ordered monoids (Rℓ-monoids) are a common generalization of, e.g., Heyting algebras and BL-algebras, i.e., algebras of intuitionistic logic and basic fuzzy logic, respectively. Modal operators (special cases of closure
operators) on Heyting algebras were studied in [MacNAB, D. S.: Modal operators on Heyting algebras, Algebra Universalis 12 (1981), 5–29] and on MV-algebras in [HARLENDEROVá,M.—RACHŮNEK, J.: Modal operators on MV-algebras, Math. Bohem. 131 (2006), 39–48]. In the paper we generalize the notion of a modal operator for general bounded commutative Rℓ-monoids and investigate their properties also for certain derived algebras.
The first author was supported by the Council of Czech Government, MSM 6198959214. 相似文献
8.
N. Christopher Phillips 《K-Theory》1989,3(5):441-478
We define a version of K-theory on the category of -C
*-algebras (countable inverse limits of C
*-algebras). Our theory is homotopy invariant, has long exact sequences and a Milnor
sequence, and satisfies Bott periodicity. On C
*-algebras it gives the ordinary K-theory, and on the space of continuous functions on a countable direct limit X of compact Hausdorff spaces, it gives the representable K-theory of X. (We do not claim that our theory is in general a representable functor.) We also define an equivariant version, and discuss several related groups.Partially supported by a National Science Foundation Postdoctoral Fellowship. 相似文献
9.
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
10.
In this note we first define the notions of (weak, strong) implicative hyper K-algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper K-ideals. Also we obtain some relations between these notions and (weak) implicative hyper K-ideals. Finally, we study the implicative hyper K-algebras of order 3, in particular we obtain a relationship between the positive implicative hyper K-algebras and (weak, strong) implicative hyper K-algebras under a simple condition. 相似文献
11.
Bounded commutative residuated ℓ-monoids are a generalization of algebras of propositional logics such as BL-algebras, i.e. algebraic counterparts of the basic fuzzy logic (and hence consequently MV-algebras, i.e. algebras of the Łukasiewicz infinite valued logic) and Heyting algebras, i.e. algebras of the intuitionistic
logic. 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. We introduce and study monadic residuated ℓ-monoids as a generalization of monadic MV-algebras.
Jiří Rachůnek was supported by the Council of Czech Goverment MSM 6198959214. 相似文献
12.
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
13.
Chun-Gil Park 《Bulletin of the Brazilian Mathematical Society》2005,36(3):333-362
Let X and Y be vector spaces. It is shown that a mapping f : X → Y satisfies the functional equation
if and only if the mapping f : X → Y is additive, and prove the Cauchy–Rassias stability of the functional equation (‡) in Banach modules over a unital C*-algebra. Let
and
be unital C*-algebras, Poisson C*-algebras, Poisson JC*-algebras or Lie JC*-algebras. As an application, we show that every almost homomorphism h :
→
of
into
is a homomorphism when h((d + 2)nuy) = h((d + 2)nu)h(y) or h((d + 2)nu ∘ y) = h((d + 2)nu) ∘ h(y) for all unitaries u ∈
, all y ∈
, and n = 0, 1, 2, • • • .
Moreover, we prove the Cauchy–Rassias stability of homomorphisms in C*-algebras, Poisson C*-algebras, Poisson JC*-algebras or Lie JC*-algebras.
Supported by Korea Research Foundation Grant KRF-2004-041-C00023. 相似文献
(‡) |
14.
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
15.
Terry A. Loring 《K-Theory》1991,4(3):227-243
Our main result is the construction of an embedding ofC(T2) into an approximately finite-dimensionalC
*-algebra which induces an injection onK
0(C(T2)). The existence of this embedding implies that Cech cohomology cannot be extended to a stable, continuous homology theory forC
*-algebras which admits a well-behaved Chern character. Homotopy properties ofC
*-algebras are also considered. For example, we show that the second homotopy functor forC
*-algebras is discontinuous. Similar embeddings are constructed for all the rational rotation algebras, with the consequence that none of the rational rotation algebras satisfies the homotopy property called semiprojectivity. 相似文献
16.
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
17.
Andrew Baker Helen Gilmour Philipp Reinhard 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2008,78(1):27-50
Topological André-Quillen homology for commutative S-algebras was introduced by Basterra following work of Kriz, and has been intensively studied by several authors. In this
paper we discuss it as a homology theory on CW commutative S-algebras and apply it to obtain results on minimal atomic p-local S-algebras which generalise those of Baker and May for p-local spectra and simply connected spaces. We exhibit some new examples of minimal atomic commutative S-algebras.
A. Baker was partially supported by a YFF Norwegian Research Council grant while at the University of Oslo in 2007–8, a Carnegie
Trust for the Universities of Scotland grant, and Intas grants 03-51-3251 and 06-1000017-8609.
H. Gilmour was supported by an EPSRC studentship.
P. Reinhard was supported by an ORS grant.
We would like to thank M. Basterra, P. Kropholler, M. Mandell, P. May, B. Richter, J. Rognes and S. Sagave for numerous helpful
comments. We are also very grateful to the referee for encouraging us to rethink significantly issues of notation and structure,
thus improving the structure of the paper. 相似文献
18.
Jonathan Rosenberg 《K-Theory》1997,12(1):75-99
We the study the algebraic K-theory of C *-algebras, forgetting the topology. The main results include a proof that commutative C*-algebras are K-regular in all degrees (that is, all theirN
T
K
iand extensions of the Fischer-Prasolov Theorem comparing algebraic and topological K-theory with finite coefficients. 相似文献
19.
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
20.
LunChuanZHANG 《数学学报(英文版)》2003,19(2):413-416
The relation between the inseparable prime C^*-algebras and primitive C^*-algebras is studied,and we prove that prime AW^*-algebras are all primitive C^*-algebras. 相似文献