1. We give a complete description of the Brown-McCoy radical of a semigroup ring R [S], where R is an arbitrary associative ring and S is a commutative cancellative semigroup; in particular we obtain the answer to a question of E. PuczyTowski stated in [11].Throughout this note all rings R are associative with unity 1; all semigroups S are commutative and cancellative with unity. Note that the condition that R and S have a unity can be dropped (cf. [8]). The quotient group of S is denoted by Q(S). We say that S is torsion free (resp. has torsion free rank n) if Q(S) is torsion free (resp. has torsion free rank n). The Brown-McCoy radical (i.e. the upper radical determined by the class of all simple rings with unity) of a ring R is denoted by %l(R). We refer to [2] for further detail on radicals and in particular on the Brown-McCoy radical.First we state some well-known results and a preliminary lemma. Let R and T be rings with the same unity such that R c T . Then T is said to be a normalizing extension of
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