Algebraic Vector Spaces

TL;DR

This paper discusses the concept of algebraic bases in vector spaces, establishing an isomorphism with a specific algebraic vector space framework, and explores potential problems inspired by this language.

Contribution

It introduces a formal language for algebraic vector spaces and demonstrates their isomorphism, highlighting conceptual clarity rather than new mathematical results.

Findings

Established an isomorphism between algebraic bases and algebraic vector spaces

Highlighted potential problems and applications of the formal language

Clarified the conceptual framework of algebraic vector spaces

Abstract

We show that the definition of an algebraic basis for a vector space allows the construction of an isomorphism with the one here called Algebraic Vector Space. Although the concept does not bring anything new, we mention some of the problems that the language established here can inspire.