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arXiv · 2303.14559

Linear Systems, Matrices and Vector Spaces over Superfields

Kaique Matias de Andrade Roberto·Hugo Rafael de Oliveira Ribeiro·Hugo Luiz Mariano·Kaique Ribeiro Prates Santos
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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.

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Kaique Matias de Andrade Roberto, Hugo Rafael de Oliveira Ribeiro, Hugo Luiz Mariano, Kaique Ribeiro Prates Santos. 2023-03-25. Linear Systems, Matrices and Vector Spaces over Superfields. https://arxiv.org/abs/2303.14559

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