Infinite hyperplane arrangements whose vertices form a lattice are studied from the point of view of commutative algebra. The quotient of such an arrangement modulo the lattice action represents the minimal free resolution of the associated binomial ideal, which defines a toric subvariety in a product of projective lines. Connections to graphic arrangements and to Beilinson’s spectral sequence ...

Let A be a unital AH-algebra and let α ∈ Aut(A) be an automorphism. A necessary condition for A ⋊α Z being embedded into a unital simple AF-algebra is the existence of a faithful tracial state. If in addition, there is an automorphism κ with κ∗1 = −idK1(A) such that α ◦ κ and κ ◦ α are asymptotically unitarily equivalent, then A⋊α Z can be embedded into a unital simple AF-algebra. Consequently,...

It is shown that every  almost linear bijection $h : Arightarrow B$ of a unital $C^*$-algebra $A$ onto a unital$C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in A$, all $y in A$, and all $nin mathbb Z$, andthat almost linear continuous bijection $h : A rightarrow B$ of aunital $C^*$-algebra $A$ of real rank zero onto a unital$C^*$-algebra...

In this paper we generalize the notion of Semi-continuity and MS-continuity and go on to study Semi-compactness, Semi-cocompactness, Semi-stability and Semi-costability in a ditopological texture space. We also extends the notion of Semi-compactness and Semi-cocompactness to a ditopological texture space modulo an ideal [13].

We prove a version of the five lemma which is useful for the study of boundary value problems for partial differential equations. The results are given in the category % of Banach spaces and bounded linear operators, and all conditions are stated modulo an arbitrary ideal of 9>. We also show that the results are valid in more general categories.

1.1. Definitions. 1) A (non-commutative) probability space consists of a pair (A, φ), where • A is a unital algebra • φ : A → C is a unital linear functional, i.e. in particular φ(1) = 1 2) Unital subalgebras A1, . . . ,An ⊂ A are called free, if we have φ(a1 . . . ak) = 0 whenever ai ∈ Aj(i) (i = 1, . . . , k) j(1) 6= j(2) 6= · · · 6 = j(k) φ(ai) = 0 (i = 1, . . . , k) 3) Random variables x1, ...

and Applied Analysis 3 Lemma 2.2 see 5, Theorem 3.3 , 6, Theorem 3.3 . Let A be a simple unital C∗-algebra. If TRR A 0, then RR A 0. If Tsr A 1 and has the (SP)-property, then tsr A 1. Definition 2.3 see 13, Definition 1.2 . Let A be an infinite dimensional finite simple separable unital C∗-algebra, and let α : G → Aut A be an action of a finite group G on A. We say that α has the tracial Rokhl...