Linear Systems, Matrices and Vector Spaces over Superfields
Commutative Algebra
2023-03-28 v1
Abstract
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but endowed with some multivalued operations). We introduce and study matrices and determinants over a commutative superrings (roughly, a ring where the sum and product are multivalued) and study linear systems and vector spaces over superfields. As an application, we obtain a fundamental result to the development of a theory of algebraic extensions of superfields.
Cite
@article{arxiv.2303.14559,
title = {Linear Systems, Matrices and Vector Spaces over Superfields},
author = {Kaique Matias de Andrade Roberto and Hugo Rafael de Oliveira Ribeiro and Hugo Luiz Mariano and Kaique Ribeiro Prates Santos},
journal= {arXiv preprint arXiv:2303.14559},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2208.08537, arXiv:2210.03784