Finite Semigroups whose Semigroup Algebra over a Field Has a Trivial Right Annihilator
نویسندگان
چکیده
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 Si such that every semigroup algebra F[Si] has a trivial right annihilator, then the right annihilator of the semigroup algebra F[S] is also trivial. Research supported by the Hungarian NFSR grants No. K77476, NK105645. 26 Attila Nagy and Lajos Rónyai Mathematics Subject Classification: 20M30
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