Radicals of some semigroup algebras

Dales, H.G. and Strauss, Dona E. and Zelenyuk, Yevhen and Zelenyuk, Yulia (2013) Radicals of some semigroup algebras. Semigroup Forum, 87 (1). pp. 80-96. ISSN 1432-2137

Abstract

In this paper we seek to determine the Jacobson radical of certain algebras based on semigroups, and in particular on the semigroups (βS,□), where S is a cancellative, countable, abelian semigroup and βS is its Stone–Čech semigroup compactification. In particular, we wish to determine the radical of ℓ  1(βℕ).