共查询到20条相似文献，搜索用时 15 毫秒

1.

Xiaohong Zhang 《Mathematica Slovaca》2013,63(4):661-678

The aim of the paper is to investigate the relationship among

*NMV*-algebras, commutative basic algebras and*naBL*-algebras (i.e., non-associative*BL*-algebras). First, we introduce the notion of strong*NMV*-algebra and prove that- a strong
*NMV*-algebra is a residuated*l*-groupoid (i.e., a bounded integral commutative residuated lattice-ordered groupoid) - a residuated
*l*-groupoid is commutative basic algebra if and only if it is a strong*NMV*-algebra.

*NMV*-filter and prove that a residuated*l*-groupoid is a strong*NMV*-algebra (commutative basic algebra) if and only if its every filter is an*NMV*-filter. Finally, we introduce the notion of weak*naBL*-algebra, and show that any strong*NMV*-algebra (commutative basic algebra) is weak*naBL*-algebra and give some counterexamples. 相似文献2.

Marina Haralampidou Reyna María Pérez-Tiscareño 《Mediterranean Journal of Mathematics》2013,10(1):411-424

We introduce (left, right, two-sided) locally convex

*H**-algebras, and we give conditions under which an one-sided locally convex*H**-algebra turns to be a two-sided one (actually, a locally convex*H**-algebra). We also give an example of a proper right locally convex*H**-algebra with a (right) involution, which is not a left involution and an example of a proper two-sided locally convex*H**-algebra, which is not a locally convex*H**-algebra. Moreover, we connect (via an Arens-Michael decomposition) a two-sided locally*m*-convex*H**-algebra with the classical (Banach) two-sided*H**-algebras. Further, we present conditions so that the left, right involutions be continuous, and we see when a twosided locally convex*H**-algebra is a dual one. Finally, we present some properties of invariant ideals which play an important rôle in structure theory of two-sided locally convex*H**-algebras. 相似文献3.

In this paper, we introduce the notion of

*bi*-Smarandache*BL*-algebra,*bi*-weak Smarandache*BL*-algebra,*bi*-*Q*-Smarandache ideal and*bi*-*Q*-Smarandache implicative filter, we obtain some related results and construct quotient of*bi*-Smarandache*BL*-algebras via*MV*-algebras (or briefly*bi*-Smarandache quotient*BL*-algebra) and prove some theorems. Finally, the notion of*bi*-strong Smarandache*BL*-algebra is presented and relationship between*bi*-strong Smarandache*BL*-algebra and*bi*-Smarandache*BL*-algebra are studied. 相似文献4.

Takeshi Katsura 《Journal of Functional Analysis》2009,257(5):1589-127

We give various necessary and sufficient conditions for an AF-algebra to be isomorphic to a graph

*C*^{∗}-algebra, an Exel-Laca algebra, and an ultragraph*C*^{∗}-algebra. We also explore consequences of these results. In particular, we show that all stable AF-algebras are both graph*C*^{∗}-algebras and Exel-Laca algebras, and that all simple AF-algebras are either graph*C*^{∗}-algebras or Exel-Laca algebras. In addition, we obtain a characterization of AF-algebras that are isomorphic to the*C*^{∗}-algebra of a row-finite graph with no sinks. 相似文献5.

E.P Klement 《Journal of Mathematical Analysis and Applications》1982,85(2):543-565

Generalizing the definitions given by the author [

*Fuzzy Sets and Systems***4**(1980), 83–93] we introduce and study*T*-fuzzy σ-algebras,*T*being any triangular norm. The main result is that for a large class of triangular norms each*T*-fuzzy σ-algebra is generated, i.e., consists of all functions*μ*:*X*→ [0, 1] being measurable with respect to some σ-algebra on*X*. 相似文献6.

Hector Freytes 《Algebra Universalis》2013,69(2):139-166

In the framework of algebras with infinitary operations, an equational base for the category of

*σ*-complete*MV*-algebras is given. In this way, we study some particular objects as simple algebras, directly irreducible algebras, injectives, etc. A completeness theorem with respect to the standard*MV*-algebra, considered as*σ*-complete*MV*-algebra, is obtained. Finally, we apply this result to the study of*σ*-complete Boolean algebras and*σ*-complete product*MV*-algebras. 相似文献7.

We introduce a notion of Gorenstein

*R*-algebras over a commutative Gorenstein ring*R*. Then we provide a necessary and sufficient condition for a tilting complex over a Gorenstein*R*-algebra*A*to have a Gorenstein*R*-algebra*B*as the endomorphism algebra and a construction of such a tilting complex. Furthermore, we provide an example of a tilting complex over a Gorenstein*R*-algebra*A*whose endomorphism algebra is not a Gorenstein*R*-algebra. 相似文献8.

Dan LI 《数学学报(英文版)》2012,28(9):1845-1850

Extending the notion of property T of finite von Neumann algebras to general von Neumann algebras, we define and study in this paper property T** for (possibly non-unital) C* -algebras. We obtain several results of property T** parallel to those of property T for unital C* -algebras. Moreover, we show that a discrete group Γ has property T if and only if the group C* -algebra Cr* (Γ) (or equivalently, the reduced group C* -algebra Cr* (Γ)) has property T**. We also show that the compact operators K(l2 ) has property T** but c0 does not have property T**. 相似文献

9.

Qihui Li Don Hadwin Jiankui Li Xiujuan Ma Junhao Shen 《Functional Analysis and Its Applications》2016,50(1):39-47

In the paper, we consider the question as to whether a unital full amalgamated free product of quasidiagonal

*C**-algebras is itself quasidiagonal. We give a sufficient condition for a unital full amalgamated free product of quasidiagonal*C**-algebras with amalgamation over a finite-dimensional*C**-algebra to be quasidiagonal. By applying this result, we conclude that the unital full free product of two AF algebras with amalgamation over a finite-dimensional*C**-algebra is AF if there exists a faithful tracial state on each of the two AF algebras such that the restrictions of these states to the common subalgebra coincide. 相似文献10.

Subhash J Bhatt 《Proceedings Mathematical Sciences》1985,94(2-3):71-91

Consideration of quotient-bounded elements in a locally convex

*GB*^{*}-algebra leads to the study of proper*GB*^{*}-algebras viz those that admit nontrivial quotient-bounded elements. The construction and structure of such algebras are discussed. A representation theorem for a proper*GB*^{*}-algebra representing it as an algebra of unbounded Hilbert space operators is obtained in a form that unifies the well-known Gelfand-Naimark representation theorem for*C*^{*}-algebra and two other representation theorems for*b*^{*}-algebras (also calledlmc^{*}-algebras), one representing*a b*^{*}-algebra as an algebra of quotient bounded operators and the other as a weakly unbounded operator algebra. A number of examples are discussed to illustrate quotient-bounded operators. An algebra of unbounded operators constructed out of noncommutative*L*^{p}-spaces on a regular probability gauge space and the convolution algebra of periodic distributions are analyzed in detail; whereas unbounded Hilbert algebras and*L*^{w}-integral of a measurable field of*C*^{*}-algebras are discussed briefly. 相似文献11.

Yu Yandong 《Fuzzy Sets and Systems》1985,16(3):251-264

Following the suggestion made by Klement [8], an axiomatic theory of TNF-σ-algebras is given,

*T*being any measurable triangular norm and*N*any negation. Most of the results about*T*-fuzzy σ-algebbrs obtained in [8] are extended to the case of TNF-σ-algebras. Some other properties of TNF-σ-algebras are also discussed. Particularly, we point out: (1) there exists a large family of triangular norms, which contains the whole Yager family and almost the whole Sugeno family as subfamilies, such that for any negation*N*each TNF-σ-algebra is generated, and (2) given a set*U*with |*U*|?2 and a measurable triangular norm*T*, in order that for every negation*N*each TNF-σ-algebra on*U*is generated it is necessary that*T*is Archimedean. 相似文献12.

In this paper we define and study chain conditions for Hilbert

*C**-modules through their*C**-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the*C**-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of*C**-algebra with a faithful conditional expectation. 相似文献13.

Arsham Borumand Saeid Akbar Rezaei Rajab Ali Borzooei 《Mathematics in Computer Science》2013,7(3):341-352

In this paper, we introduce some types of filters in

*BE*-algebras and state some theorems which determine the relationship between these filters and other filters of a*BE*-algebra and by some examples we show that these notions are different. 相似文献14.

Ola Bratteli 《Journal of Functional Analysis》1976,21(2):195-202

It is proved that any separable abelian

*C*^{1}-algebra is the center of a*C*^{1}-algebra that is the inductive limit of an increasing sequence of finite-dimensional*C*^{1}-algebras. 相似文献15.

A. M. Bikchentaev 《Russian Mathematics (Iz VUZ)》2013,57(12):66-69

In 1975 U. Haagerup has posed the following question:

*Whether every normal subadditive weight on a W*-algebra is σ-weakly lower semicontinuous*? In 2011 the author has positively answered this question in the particular case of abelian*W**-algebras and has presented a general form of normal subadditive weights on these algebras. Here we positively answer this question in the case of finite-dimensional*W**-algebras. As a corollary, we give a positive answer for subadditive weights with some natural additional condition on atomic*W**-algebras. We also obtain the general form of such normal subadditive weights and norms for wide class of normed solid spaces on atomic*W**-algebras. 相似文献16.

The question of which

*C*^{1}-algebras have only inner derivations has been considered by a number of authors for 25 years. The separable case is completely solved, so this paper deals only with the non-separable case. In particular, we show that the*C*^{1}-tensor product of a von Neumann algebra and an abelian*C*^{1}-algebra has only inner derivations. Other special types of*C*^{1}-algebras are shown to have only inner derivations as well such as the*C*^{1}-tensor product of*L*(*H*) (all bounded operators on separable Hilbert space) and any separable*C*^{1}-algebra having only inner derivations. Derivations from a smaller*C*^{1}-algebra into a larger one are also considered, and this concept is generalized to include derivations between*C*^{1}-algebras connected by a^{1}-homomorphism. Finally, we consider the general problem of a sequence of linear functionals on a*C*^{1}-algebra which converges to zero (in norm) when restricted to any abelian*C*^{1}-subalgebra. Does such a sequence converge to zero in norm? The answer is “yes” for normal functionals on*L*(*H*), but unknown in general. 相似文献17.

We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~*-algebra. Then, the crossed product C~*-algebra C~*(G, A, α) has tracia rank zero(or has tracial rank no more than one). In fact,we get a more general results. 相似文献

18.

In this paper, we will define several new isomorphism invariants for

*C**-algebras by hyponormal partial isometries and discuss the relation between these invariants and*K*-theory of*C**-algebras. This study was in part inspired by the work of H. Lin and H. Su in the context of \({A\mathcal{T}}\)-algebras. An \({{\rm A}\mathcal{T}}\)-algebra often becomes an extension of an \({{\rm A}\mathbb{T}}\)-algebra by an AF-algebra. We show that there is an essential extension of a simple \({{\rm A}\mathbb{T}}\)-algebra which has real rank zero by an AF-algebra such that it has real rank zero and is not an \({A\mathcal{T}}\)-algebra. 相似文献19.

Andrew Percy 《Expositiones Mathematicae》2003,21(1):47-62

The homotopy Π-algebra of a pointed topological space,

*X*, consists of the homotopy groups of*X*together with the additional structure of the primary homotopy operations. We extend two well-known results for homotopy groups to homotopy Π-algebras and look at some examples illustrating the depth of structure on homotopy groups; from graded group to graded Lie ring, to Π-algebra and beyond. We also describe an abstract Π-algebra and give three abstract Π-algebra structures on the homotopy groups of the loop space of*X*which can be realized as the homotopy Π-algebras of three different spaces. 相似文献20.

A pro-

*C**-algebra is a (projective) limit of*C**-algebras in the category of topological *-algebras. From the perspective of non-commutative geometry, pro-*C**-algebras can be seen as non-commutative*k*-spaces. An element of a pro-*C**-algebra is*bounded*if there is a uniform bound for the norm of its images under any continuous *-homomorphism into a*C**-algebra. The *-subalgebra consisting of the bounded elements turns out to be a*C**-algebra. In this paper, we investigate pro-*C**-algebras from a categorical point of view. We study the functor (−)_{ b }that assigns to a pro-*C**-algebra the*C**-algebra of its bounded elements, which is the dual of the Stone-Čech-compactification. We show that (−)_{ b }is a coreflector, and it preserves exact sequences. A generalization of the Gelfand duality for commutative unital pro-*C**-algebras is also presented. 相似文献