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}.

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}.

This paper seeks ring-theoretic conditions of an integral domain R that reflect in the Clifford property or Boolean property of its class semigroup S(R), that is, the semigroup of the isomorphy classes of the nonzero (integral) ideals of R with the operation induced by multiplication. Precisely, in Section 3, we characterize integrally closed domains with Boolean class semigoup; in this case, S...

We study algebraic and topological properties of the convolution semigroups of probability measures on topological groups and show that a compact Clifford topological semigroup S embeds into the convolution semigroup P (G) over some topological group G if and only if S embeds into the semigroup exp(G) of compact subsets of G if and only if S is an inverse semigroup and has zero-dimensional maxi...

Bazzoni’s Conjecture states that the Prüfer domain R has finite character if and only if R has the property that an ideal of R is finitely generated if and only if it is locally principal. In [4] the authors use the language and results from the theory of lattice-ordered groups to show that the conjecture is true. In this article we supply a purely ring theoretic proof. 1. Bazzoni’s Conjecture ...

The t-class semigroup of an integral domain is the semigroup of the isomorphy classes of the t-ideals with the operation induced by ideal t-multiplication. This paper investigates ring-theoretic properties of an integral domain that reflect reciprocally in the Clifford or Boolean property of its t-class semigroup. Contexts (including Lipman and Sally-Vasconcelos stability) that suit best t-mult...

The t-class semigroup of an integral domain is the semigroup of the isomorphy classes of the t-ideals with the operation induced by ideal tmultiplication. This paper investigates ring-theoretic properties of an integral domain that reflect reciprocally in the Clifford or Boolean property of its t-class semigroup. Contexts (including Lipman and Sally-Vasconcelos stability) that suit best t-multi...

The t-class semigroup of an integral domain is the semigroup of the isomorphy classes of the t-ideals with the operation induced by ideal t-multiplication. This paper investigates ring-theoretic properties of an integral domain that reflect reciprocally in the Clifford or Boolean property of its t-class semi-group. Contexts (including Lipman and Sally-Vasconcelos stability) that suit best t-mul...

Let $S$ be an inverse semigroup and let $E$ be its subsemigroup of idempotents. In this paper we define the $n$-th module cohomology group of Banach algebras and show that the first module cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ we show that $HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach sp...