Abstract
In this paper, we study the cellularity of some semigroup algebras. We show that the semigroup algebra of a U-semiabundant semigroup with Rees matrix semigroups over monoids as its principal \(\sim _U\)-factors is a cellular algebra if and only if all of the monoid algebras are cellular. We also study the cellularity of the semigroup algebra of a semilattice of Rees matrix semigroups. As consequences, we get the cellularity of super abundant semigroup algebras and complete regular semigroup algebras.
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