An introduction to Noncommutative Projective Geometry
by D. Rogalski
Publisher: arXiv 2014
Number of pages: 55
These notes are an expanded version of the author's lectures at the graduate workshop 'Noncommutative Algebraic Geometry' at the Mathematical Sciences Research Institute in June 2012. The main topics discussed are Artin-Schelter regular algebras, point modules, and the noncommutative projective scheme associated to a graded algebra.
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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 E.B. Elliott - The Clarendon Press
The primary object of this book is that of explaining with all the clearness at my command the leading principles of invariant algebra, in the hope of making it evident to the junior student that the subject is attractive as well as important.
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From the contents: Free groups; Ordered sets, induction, and the Axiom of Choice; Lattices, closure operators, and Galois connections; Categories and functors; Universal constructions in category-theoretic terms; Varieties of algebras; etc.
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These are lecture notes for a course on the theory of Clifford algebras. The various applications include vector space and projective geometry, orthogonal maps and spinors, normed division algebras, as well as simplicial complexes and graph theory.