Units and linear independence

Abstract

An algebra [Formula: see text] will be called fluid if for any linearly independent set [Formula: see text] consisting of units, the set [Formula: see text] of inverses of the elements of [Formula: see text] is also linearly independent. We consider various examples of fluid algebras and study fluid algebras in some specific settings including direct sums, field extensions, quotient rings of the ring of polynomials over a field, and matrix algebras. Pertinent parameters for the study of fluidity are also introduced and studied.