The aim of this article is to present a detailed algebraic computation of the Hochschild and cyclic homology groups of the Yang–Mills algebras YM(n) (n ∈ ℕ≧2) defined by A. Connes and M. Dubois-Violette in [8], continuing ...

We introduce a version of discrete Morse theory for posets. This theory studies the topology of the order complexes K(X) of h-regular posets X from the critical points of admissible matchings on X. Our approach is related ...

We develop a new method to compute the homology groups of Alexandroff topological spaces (or equivalently of partially ordered sets) by means of spectral sequences giving a complete and simple description of the corresponding ...

Let f: A → B be a ring homomorphism of not necessarily unital rings and I A an ideal which is mapped by f isomorphically to an ideal of B. The obstruction to excision in K-theory is the failure of the map between relative ...

We prove without any assumption on the ground field that higher Hochschild homology groups do not vanish for two large classes of algebras whose global dimension is not finite.

Based on the cohomology theory of groups, Andrade and Fanti defined in [1] an algebraic invariant, denoted by E(G,S, M), where G is a group, S is a family of subgroups of G with infinite index and M is a Z2G-module. In ...

We develop the homology theory of CW (A)-complexes, generalizing the classical cellular homology theory for CW-complexes. A CW (A)-complex is a topological space which is built up out of cells of a certain core A.

This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida ...