In this paper, we prove the conjectures made in a joint paper of the author with Carlson and Robinson, on the vanishing of cohomology of a nite group G. In particular, we prove that if k is a eld of characteristic p, then every non-projective kG-module M in the principal block has nontrivial cohomology in the sense that H (G;M) 6= 0, if and only if the centralizer in G of every element of order...

In this paper, we prove the conjectures made in a joint paper of the author with Carlson and Robinson, on the vanishing of cohomology of a nite group G. In particular, we prove that if k is a eld of characteristic p, then every non-projective kG-module M in the principal block has nontrivial cohomology in the sense that H (G; M) 6 = 0, if and only if the centralizer in G of every element of ord...

Let mod kG be the stable category of finitely generated modular representations of a finite group G over a field k. We prove a Krull-Remak-Schmidt theorem for thick subcategories of mod kG. It is shown that every thick tensor-ideal C of mod kG (i.e. a thick subcategory which is a tensor ideal) has a (usually infinite) unique decomposition C = ∐ i∈I Ci into indecomposable thick tensor-ideals. Th...

The main source of inspiration for the present paper is the work of R. Rosebrugh and R.J. Wood on constructively completely distributive lattices where the authors elegantly employ the concepts of adjunction and module. Both notions (suitably adapted) are available in topology too, which permits us to investigate topological, metric and other kinds of spaces in a similar spirit. We introduce he...

One of the factors that is hindering adoption nonmonotonic description logics in applications performance. Even when monotonic and inferences have same asymptotic complexity, implementation reasoning may be significantly slower. This happens also with family DLN. In this work we address issue by introducing two optimizations for The first optimization, called optimistic evaluation, aims at expl...