Finite semigroups whose semigroup algebra over a field has a trivial right annihilator
Attila László Nagy, Lajos Rónyai · International Journal of Contemporary Mathematical Sciences · 2013
An element a of a semigroup algebra F[S] over a field F is called a right annihilating element of F[S] if xa = 0 for every x ∈ F[S], where 0 denotes the zero of F[S].The set of all right annihilating elements of F[S] is called the right annihilator of F[S].In this paper we show that, for an arbitrary field F, if a finite semigroup S is a direct product or semilattice or right zero semigroup of semigroups S i such that every semigroup algebra F[S i ] has a trivial right annihilator, then the right annihilator of the semigroup algebra F[S] is also trivial.