We show that the biflatness—in the sense of A. Ya. Helemskĭı—of the Fourier algebra A(G) of a locally compact groupG forcesG to either have an abelian subgroup of finite index or to be non-amenable without containing F2 as a closed subgroup. An analogous dichotomy is obtained for biprojectivity.

In the present paper, we consider biflatness of certain classes of semigroupalgebras. Indeed, we give a necessary condition for a band semigroup algebra to bebiflat and show that this condition is not sufficient. Also, for a certain class of inversesemigroups S, we show that the biflatness of ell^{1}(S)^{primeprime} is equivalent to the biprojectivity of ell^{1}(S).

in the present paper, we consider biflatness of certain classes of semigroupalgebras. indeed, we give a necessary condition for a band semigroup algebra to bebiflat and show that this condition is not sufficient. also, for a certain class of inversesemigroups s, we show that the biflatness of ell^{1}(s)^{primeprime} is equivalent to the biprojectivity of ell^{1}(s).

We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, L (G), and the Fourier algebra, A(G), of a locally compact group, G. Barry Johnson introduced the important concept of amenability for Banach algebras in [20], where he proved, among many other things, that a group algebra L1(G) is amenable precisely when the locally ...

In this paper, we study an approximate biflatness of l 1 S , where id="M2"> is a Clifford semigroup. Indeed, show that semigroup algebra id="M3"> approximately biflat if and only every maximal subgroup id="M4"> amenable...