Properties of Slender Rings

Slender rings and their products are characterized in terms of algebraic and topological properties. Possible limitations on uncountable products of such rings are discussed. Ring, module, and topological terminology and notation are standard. R denotes a unital ring with identity 1, and R ω denotes its countable product, that is, the set of all sequences of elements of R. Of course ω {0, 1,. . .}. R ω is both a left and right R-module; it will be treated as a left R-module unless otherwise stated. Results for left R-modules carry over mutatis mutandis to right R-modules.