An introduction to Algebra and Topology
by Pierre Schapira
Publisher: University of Luxemburg 2012
Number of pages: 78
These lecture notes are an elementary introduction to the language of categories and sheaves. From the table of contents: Linear algebra over a ring; The language of categories; Sheaves (Flabby sheaves and soft sheaves, Cohomology of sheaves).
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by George B. Seligman - American Mathematical Society
The purpose of the present memoir is to demonstrate the applicability, under certain restrictions on the algebra and the base field, of the techniques used in the determination of all simple Lie algebras of characteristic zero.
by Leonard Evens - Northwestern University
Contents: Groups; Group actions on sets; Normal series; Ring theory; Modules; Hom and tensor; Field theory; Galois theory; Applications of Galois theory; Infinite extensions; Categories; Multilinear algebra; More ring theory; Localization; etc.
by S. Montgomery, H. Schneider - Cambridge University Press
Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras, and other areas. The book gives a clear picture of the current trends, with a focus on what will be important in future research.
by Michael Artin
From the table of contents: Morita equivalence (Hom, Bimodules, Projective modules ...); Localization and Goldie's theorem; Central simple algebras and the Brauer group; Maximal orders; Irreducible representations; Growth of algebras.