Abstract A split system $$\mathcal S$$ S on a finite set X , $$|X|\ge 3$$ | X ≥ 3 is of bipartitions or splits which contains all the form $$\{x,X-\{x\}\}$$ { x , <mml:...

An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

By a partial dynamical system we mean a pair (X,α) where X is compact and α : ∆ → X is a continuous, not necessarily injective, mapping such that ∆ is clopen, additionally we assume that α(∆) is open. Such systems arise naturally when dealing with commutative C∗-dynamical system (A, δ). We associate with every pair (X,α), or (A, δ), a covariance C∗-algebra C∗(X,α) = C∗(A, δ) which agrees with a...

Let A be a unital separable C∗-algebra, and D a K1-injective strongly selfabsorbing C∗-algebra. We show that if A is D-absorbing, then the crossed product of A by a compact second countable group or by Z or by R is D-absorbing as well, assuming the action satisfying a Rokhlin property. In the case of a compact Rokhlin action we prove a similar statement about approximate divisibility.

Let \({\varvec{\Gamma }} = (V,E)\) be a (non-trivial) finite graph with \(\lambda : E \rightarrow {\mathbb {R}}_{+}\) an edge labeling of }}\). \(\rho V\rightarrow {R}}^{2}\) map which preserves the labeling, i.e., $$\begin{aligned} \Vert \rho (u) - (v)\Vert _{2} \lambda ((u,v)), \,\forall (u,v)\in E, \end{aligned}$$where \(\Vert x-y\Vert _{2}\) denotes Euclidean distance between two points \(x...

The injective tensor product of normal representable bimodules over von Neumann algebras is shown to be normal. The usual Banach module projective tensor product of central representable bimodules over an Abelian C∗-algebra is shown to be representable. A normal version of the projective tensor product is introduced for central normal bimodules.