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1	Torsion Products of Modules Over the Orbit Category Keiper, Graham January 2016 (has links) The goal of this paper is to extend Sanders Mac Lane's formulation of the torsion product as equivalence classes of projective chain complexes in the setting of modules over a ring to the setting of modules over small categories. The motivation to extend the definition was with a specific view to the orbit category. The main difficulty was in defining an appropriate dual for modules over small categories. During the course of our investigation it was discovered that modules over small categories can be formulated as modules over a matrix ring without losing any of the key features. / Thesis / Master of Science (MSc) Modules Over Small Categories Orbit Category Torsion Product Tor Category Theory Derived Functors Homological Algebra Matrix Ring
2	Ideais em anéis de matrizes finitos e aplicações à Teoria de Códigos / Ideals in finite matrix rings and applications to Coding Theory Taufer, Edite 19 January 2018 (has links) Neste trabalho damos uma descrição completa dos ideais à esquerda em anéis de matrizes sobre corpos finitos. Aplicamos estes resultados ao estudo de álgebras de grupo de uma família particular de grupos indecomponíveis e mostramos como construir códigos corretores de erros como ideais destas álgebras. Em particular, exibimos exemplos de códigos tais que, para um dado comprimento e uma dada dimensão, têm o melhor peso possível. / In this work we give a complete description of the left ideals in the full ring of matrices over a finite field. We apply these results to the study of group algebras of a given family of indecomposable groups and show how to construct error correcting codes as ideals of these algebras. In particular, we exhibit examples of codes such that, for a given length and a given dimension, have the best possible weight. Álgebra de grupo Anel de matrizes Best code Código de grupo Códigos corretores de erros Corpo finito Error correcting codes Finite field Group algebra Group code Matrix ring Melhor código

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Torsion Products of Modules Over the Orbit Category

Ideais em anéis de matrizes finitos e aplicações à Teoria de Códigos / Ideals in finite matrix rings and applications to Coding Theory