in this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric connes amenability. we determine symmetric module amenability and symmetric connes amenability of some concrete banach algebras. indeed, it is shown that $ell^1(s)$ is  a symmetric $ell^1(e)$-module amenable if and only if $s$ is amenable, where $s$ is an inverse semigroup with subsemigr...

Numerical semigroup rings are investigated from the relative viewpoint. It is known that algebraic properties such as singularities of a numerical ring flat algebra. In this paper, we show arithmetic and set-theoretic an equi-gcd

The concept of amenability for Banach algebras was introduced by Johnson in 1972 [6]. Several modifications of this notion, such as approximate amenability and pseudo-amenability, were introduced in [2] and [4]. In the current paper we investigate the pseudo-amenability of Brandt semigroup algebras. It was shown in [2] and [4] that for the group algebra L(G), amenability, approximate amenabilit...

Denote by PSelf Ω (resp., Self Ω) the partial (resp., full) transformation monoid over a set Ω, and by SubV (resp., EndV ) the collection of all subspaces (resp., endomorphisms) of a vector space V . We prove various results that imply the following: (1) If cardΩ > 2, then Self Ω has a semigroup embedding into the dual of Self Γ iff card Γ > 2 . In particular, if Ω has at least two elements, th...

In [2], Bost and Connes studied a particular Hecke C-algebra CQ arising in number theory. The algebra CQ can be realised as a semigroup crossed product C (Q/Z)⋊αN ∗ by an endomorphic action α of the multiplicative semigroup N on the group Calgebra C(Q/Z) [7], and this realisation has provided useful insight into the analysis of CQ [5, 13]. Since individual elements of Q/Z and N ∗ involve only f...