the aim of this paper is to generalize the‎‎notion of pseudo-almost valuation domains to arbitrary‎ ‎commutative rings‎. ‎it is shown that the classes of chained rings‎ ‎and pseudo-valuation rings are properly contained in the class of‎ ‎pseudo-almost valuation rings; also the class of pseudo-almost‎ ‎valuation rings is properly contained in the class of quasi-local‎ ‎rings with linearly ordere...

In this paper, we introduce a concept of an evacuation scheme on the Cayley graph infinite finitely generated group. This is collection simple paths bringing all vertices to infinity. We impose restriction that every edge can be used uniformly bounded number times in scheme. An easy observation shows existence such equivalent non-amenability A special case happens if only once. These schemes ar...

Let G be a locally compact group, and let 1 < p < ∞. In this paper we investigate the injectivity of the left L1(G)-module Lp(G). We define a family of amenability type conditions called (p, q)-amenability, for any 1 ≤ p ≤ q. For a general locally compact group G we show if Lp(G) is injective, then G must be (p, p)-amenable. For a discrete group G we prove that l p(G) is injective if and only i...

The present paper deals with the concept of left amenability for a wide range of Banach algebras known as Lau algebras. It gives a fixed point property characterizing left amenable Lau algebras in terms of left Banach -modules. It also offers an application of this result to some Lau algebras related to a locally compact group G, such as the Eymard-Fourier algebra A(G), the Fourier-Stieltjes al...