Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

We consider the space of weakly almost periodic functions on a transformation semigroup (S, X , ?) and show that if X is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of S on X, then every continuous function on X, vanishing at infinity is weakly almost periodic. We also use a number of diverse examples to show ...

we consider the space of weakly almost periodic functions on a transformation semigroup (s, x , ?) and show that if x is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of s on x, then every continuous function on x, vanishing at infinity is weakly almost periodic. we also use a number of diverse examples to show that th...

In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras.Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras.In the following we studythe...

primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. in fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly.  in this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pr...

we show that every semi-artinian module which is contained in a direct sum of finitely presented modules in $si[m]$, is weakly co-semisimple if and only if it is regular in $si[m]$. as a consequence, we observe that every semi-artinian ring is regular in the sense of von neumann if and only if its simple modules are $fp$-injective.

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Primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. In fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly.  In this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pr...