Vector subspaces of finite fields and star operations on pseudo-valuation domains

Abstract

Given an extension of finite fields F⊆L, we study the number of the equivalence classes of F-vector subspaces of L modulo multiplication by elements of L, obtaining an exact formula and some bounds. We then apply the results obtained to the study of the set of F-star operations on L, which correspond to star operations on a pseudo-valuation domain R.