Let A be a unital C*-algebra. We describe K-skeleton factorizations of all invertible operators on a Hilbert C*-module HA, in particular on H = l 2, with the Fredholm index as an invariant. We then outline the isomorphisms K0(A) ∼= π2k([p]0) ∼= π2k(GL p r(A)) and K1(A) ∼= π2k+1([p]0) ∼= π2k+1(GL p r(A)) for k ≥ 0, where [p]0 denotes the class of all compact perturbations of a projection p in th...

Let j/ be a unital C*-algebra. We describe K-skeleton factorizations of all invertible operators on a Hubert C*-module %^ , in particular on «^ = I2 , with the Fredholm index as an invariant. We then outline the isomorphisms K0(s/) =i TC2k([p]0) 3 n2k(GLp(s/)) and Kx(s*) & ä2*+i([Pjo) = n2k+\(GLpr(s?)) for k > 0 , where [p]o denotes the class of all compact perturbations of a projection p in th...

Let R be a commutative integral domain with quotient field K and let P be a nonzero strongly prime ideal of R. We give several characterizations of such ideals. It is shown that (P : P) is a valuation domain with the unique maximal ideal P. We also study when P^{&minus1} is a ring. In fact, it is proved that P^{&minus1} = (P : P) if and only if P is not invertible. Furthermore, if P is invertib...

The endomorphism ring of the group of all sequences of integers, the Baer-Specker group, is isomorphic to the ring of row finite infinite matrices over the integers. The product bases of that group are represented by the multiplicative group of invertible elements in that matrix ring. All products in the Baer-Specker group are characterized, and a lemma of László Fuchs regarding such products i...

Generalizing the case of an infinite discrete metric space finite diameter, we say that a (X,d) is Kuiper space, if group invertible elements its uniform Roe algebra norm-contractible. Various sufficient conditions on to be or not are obtained.

We consider discrete invertible dynamical systems L with the property that the kth iterate L k possesses (reversing) symmetries that are not possessed by L. A map U is called a (reversing) k-symmetry of L if k is the smallest positive integer for which U is a (reversing) symmetry of L k. In this paper we discuss the particular case that L possesses a cyclic reversing k-symmetry group. We derive...