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Scitus Academics LLC Introduction to Noncommutative Algebra

Name: Introduction to Noncommutative Algebra
Brand: Scitus Academics LLC
Price: 42.39 GBP
Availability: InStock

Algebra

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Description

A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which xy does not always equal yx; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions. The main motivation is to extend the commutative duality between spaces and functions to the noncommutative setting. In mathematics, spaces, which are geometric in nature, can be related to numerical functions on them. In general, such functions will form a commutative ring. For instance, one may take the ring C(X) of continuous complex-valued functions on a topological space X. In many cases, we can recover X from C(X), and therefore it makes some sense to say that X has commutative topology. The dream of noncommutative geometry is to generalize this duality to the duality between noncommutative algebras, or sheaves of noncommutative algebras, or sheaf-like noncommutative algebraic or operator-algebraic structures and geometric entities of certain kind, and interact between the algebraic and geometric description of those via this duality. Regarding that the commutative rings correspond to usual affine schemes, and commutative C*-algebras to usual topological spaces, the extension to noncommutative rings and algebras requires non-trivial generalization of topological spaces, as "non-commutative spaces". This book provides an elementary introduction to noncommutative rings and algebras.

Product Specifications

Brand: Scitus Academics LLC
Format: Hardcover
ASIN: 1681171880
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 01 January 2016
Listed Since: 05 February 2016

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Scitus Academics LLC Introduction to Noncommutative Algebra

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