Radicals of some semigroup algebras

In this paper we seek to determine the Jacobson radical of certain algebras based on semigroups, and in particular on the semigroups $(βS, \Box)$, 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 $\ell^{ 1}(β\N)$.

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