Uniform algebras satisfying certain extension properties

Ring Theoretic Properties of Certain Hecke Algebras

In the work of one of us (A.W.) on the conjecture that all elliptic curves defined over Q are modular, the importance of knowing that certain Hecke algebras are complete intersections was established. The purpose of this article is to provide the missing ingredient in [W2] by establishing that the Hecke algebras considered there are complete intersections. As is recorded in [W2], a method going...

On congruence extension properties for ordered algebras

Extension Properties of Boolean Contact Algebras

We show that the class of Boolean contact algebras has the joint embedding property and the amalgamation property, and that the class of connected Boolean contact algebras has the joint embedding property but not the amalgamation property.

Derivations on Certain Semigroup Algebras

In the present paper we give a partially negative answer to a conjecture of Ghahramani, Runde and Willis. We also discuss the derivation problem for both foundation semigroup algebras and Clifford semigroup algebras. In particular, we prove that if S is a topological Clifford semigroup for which Es is finite, then H1(M(S),M(S))={0}.

Biflatness of certain semigroup algebras

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).