We show that the following five categories are equivalent: (1) opposite category of commutative von Neumann algebras; (2) compact strictly localizable enhanced measurable spaces; (3) locales; (4) hyperstonean (5) spaces. This result can be seen as a measure-theoretic counterpart Gelfand duality between unital C*-algebras and Hausdorff topological

We show that the image of a commutative monotone sequentially complete C∗-algebra, under a sequentially normal morphism, is again a monotone sequentially complete C-algebra, and also a monotone sequentially closed C∗-subalgebra. As a consequence, the image of an algebra of this type, under a sequentially normal representation in a separable Hilbert space, is strongly closed. In the case of a un...

1. Non-commutative probability spaces In general, a non-commutative probability space is a pair (A, τ), where A is a unital algebra (over the field of complex numbers C) and τ a linear functional with τ(I) = 1, where I is the identity of A. Elements of A are called random variables. Since positivity is a key concept in (classical) probability theory, this can be captured by assuming that A is a...

The paper considers the role of quantale algebra nuclei in representation of quotients of quantale algebras, and in factorization of quantale algebra homomorphisms. The set of all nuclei on a given quantale algebra is endowed with the structure of quantale semi-algebra.

We introduce a new concept of the bounded rank (with respect to a positive constant) for unital C∗-algebras as a modification of the usual real rank. We present a series of conditions insuring that bounded and real ranks coincide. These observations are then used to prove that for a given n and K > 0 there exists a separable unital C∗-algebra Z n such that every other separable unital C∗-algebr...

Let $G$ be a finite groupoid and $\alpha=(S_g,\alpha_g)_{g\in G}$ unital partial action of group-type on commutative ring $S=\oplus_{y\in G_0}S_y$. We prove Galois correspondence between class wide subgroupoids subrings $S$. recover known results for global actions we give several examples to illustrate the correspondence.

Tensor product of highest weight modules and intermediate for Virasoro algebra have been studied around 1997. Since then the irreducibility problem tensor is open. We consider loop-Virasoro [Formula: see text], where Vir text] a commutative associative unital over text]. In this paper, we study Finally found out necessary sufficient condition such to be isomorphic.

Let R be a commutative unital finite rings and Z(R) its set of zero divisors. The study automorphisms algebraic structures via divisor graphs is still an active area research. Perhaps, because the fact that have got real life application in capturing symmetries structures. In this study, such which product any four has been determined.

In this work, all rings under consideration will be assumed to commutative with nonzero identity and modules unital. We introduce the concept of Restrict Nearly primary finitely compactly packed modules, which generalizes modules. find conditions that make packed. Also, several results on are proved. addition, necessary sufficient for an ℛ−module