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Pseudonormability of topological semigroup rings

The problem of norming (pseudonorming) algebraic objects with a topology often occupies the attention of mathematicans. Thus, questions of the pseudonormability of topological vector spaces are studied in detail in functional analysis, and a chapter in [1] is devoted to the analogous question for rings. For semigroup rings, this problem was considered in [2], and it was conjectured that the topology of a monoid induced by the topology of a pseudonormable semigroup ring of this monoid is discrete. In this paper we shall give a criterion for a topological ring and a topological monoid to have a pseudonormable semigroup ring. We shall also show that the conjecture^ 1 ' in [4] is false in the general case. Throughout what follows we shall consider multiplicative monoids containing 0. In the ring R[G] the zeros and unities of the coefficient ring and the monoid coincide.