Pseudocompact refinements of compact ring topologies

In this paper, results of Tsarelunga resp. Comfort, Szambien and the first-listed author are improved. Throughout this abstract, (R, T) denotes a nonmetrizable compact ring. First a main tool is shown: If (R, T) is topologically nilpotent, then w(R) = w(R/(R) over bar (2)) holds. By using tensor products of unitary modules it is proved that every nonmetrizable compact ring with an identity has a proper pseudocompact refinement. (R, T) admits exactly 2(2)(vertical bar R vertical bar) -many pseudocompact ring topologies on R finer than T in the following cases: R is a commutative local ring; (R, T) is topologically nilpotent; (R, T) is commutative such that w(R, T) is a regular cardinal number. (C) 2019 Elsevier B.V. All rights reserved.