We define the cohomological Burnside ring B(G,M) of a finite group G with coefficients in a ZG-module M as the Grothendieck ring of the isomorphism classes of pairs [X, u] where X is a G-set and u is a cohomology class in a cohomology group H X(G,M). The cohomology groups H ∗ X(G,M) are defined in such a way that H∗ X(G, M) ∼= ⊕iH∗(Hi,M) when X is the disjoint union of transitive G-sets G/Hi. I...

1 Let G be a finite group. The Burnside ring B(G) of the group G is one of the fundamental representation rings of G, namely the ring of permutation representations. It is in many ways the universal object to consider when looking at the category of G-sets. It can be viewed as an analogue of the ring Z of integers for this category. It can be studied from different points of view. First B(G) is...

We introduce a theory of modules over representation small category taking values in entwining structures semiperfect coalgebra. This takes forward the aim developing categories entwined to same extent as that module well philosophy Mitchell working with rings several objects. The representations are motivated by work Estrada and Virili, who developed preadditive categories, which were then stu...

in this paper $s$ is a monoid with a left zero and $a_s$ (or $a$) is a unitary right $s$-act. it is shown that a monoid $s$ is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right $s$-act is quasi-projective. also it is shown that if every right $s$-act has a unique zero element, then the existence of a quasi-projective cover for each right act implies that ...

how to cite this article: shetty g, avabratha k.s, rai b.s. ring-enhancing lesions in the brain: a diagnostic dilemma. iran j child neurol. 2014 summer;8(3): 61-64. abstract the most common radiological abnormality seen in young indian patients with epilepsy is single small enhancing (ring/disc) computed tomographic (ct) lesions. the two most common differential diagnosis of this lesion in clin...

let  $r$ be a commutative noetherian ring and $i$ be an ideal of $r$. we say that $i$ satisfies the persistence property if  $mathrm{ass}_r(r/i^k)subseteq mathrm{ass}_r(r/i^{k+1})$ for all positive integers $kgeq 1$, which $mathrm{ass}_r(r/i)$ denotes the set of associated prime ideals of $i$. in this paper, we introduce a class of square-free monomial ideals in the polynomial ring  $r=k[x_1,ld...