2023/09/18 by Anuj Kumar Bhagat, Bhagat, Anuj Kr, Ritumoni Sarma +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Computer and information sciences #Information Theory (cs.IT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2309.09595
openalex publication_date 2023/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A non-zero \mathbbF-valued \mathbbF-linear map on a finite dimensional \mathbbF-algebra is called an \mathbbF-valued trace if its kernel does not contain any non-zero ideals. However, given an \mathbbF-algebra such a map may not always exist. We find an infinite class of finite-dimensional commutative \mathbbF-algebras which admit an \mathbbF-valued trace. In fact, in these cases, we explicitly construct a trace map. The existence of an \mathbbF-valued trace on a finite dimensional commutative \mathbbF-algebra induces a non-degenerate bilinear form on the \mathbbF-algebra which may be helpful both theoretically and computationally. In this article, we suggest a couple of applications of an \mathbbF-valued trace map of an \mathbbF-algebra to algebraic coding theory.