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- Title
Units and linear independence.
- Authors
López-Permouth, Sergio R.; Moore, Jeremy; Pilewski, Nick; Szabo, Steve
- Abstract
An algebra A will be called fluid if for any linearly independent set X consisting of units, the set X − 1 of inverses of the elements of X 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.
- Subjects
LINEAR dependence (Mathematics); QUOTIENT rings; MATRICES (Mathematics); POLYNOMIAL rings; INDEPENDENT sets; ALGEBRA
- Publication
Journal of Algebra & Its Applications, 2024, Vol 23, Issue 8, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498825500495