in this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (k, ?) are equivalent. for a normal subgroup h of k, we define a weight function ?? on kih and obtain connection between left amenability of (k, ?) and (k|h, ??). let h be a compact subhypergroup of k. we define the weight function on k||h and obtain connection betw...

Let A be a ring of dimension d containing an infinite field k, T1,…,Tr variables over and P projective A[T1,…,Tr]-module rank n. Assume one the following conditions holds. 2n≥d+3 is extended from A. 2n≥d+2, affine F‾p-algebra singular locus Spec(A) closed set V(J) with ht J≥d−n+2.

Let φ be a w-continuous homomorphism from a dual Banach algebra to C. The notion of φ-Connes amenability is studied and some characterizations is given. A type of diagonal for dual Banach algebras is dened. It is proved that the existence of such a diagonal is equivalent to φ-Connes amenability. It is also shown that φ-Connes amenability is equivalent to so-called φ-splitting of a certain short...

We first show that co-amenability does not pass to subgroups, answering a question asked by Eymard in 1972. We then address address coamenability for von Neumann algebras, describing notably how it relates to the former. Co-amenable subgroups A subgroup H of a group G is called co-amenable in G if it has the following relative fixed point property: Every continuous affine G-action on a convex c...

In 2005, A. Abdollahi and A. Rejali, studied the relations betweenparadoxical decomposition and configuration for semigroups. In thepresent paper, we introduce one other concept of amenability typeon semigroups and groups which includes amenability of semigroupsand inner-amenability of groups. We have extend the previous knownresults to semigroups and groups satisfying this concept.

Let e 2n denote the subposet obtained by selecting even ranks in the partition lattice 2n : We show that the homology of e 2n has dimension (2n)! 2 2n?1 E 2n?1 ; where E 2n?1 is the tangent number. It is thus an integral multiple of both the Genocchi number and an Andr e or simsun number. Using the general theory of rank-selected homology representations developed in Su], we show that, for the ...