Introduction to Noncommutative Algebra - Rilegato

Rilegato

ISBN 10: 1681171880 ISBN 13: 9781681171883

Casa editrice: Scitus Academics Llc, 2016

Riassunto

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.

Dettagli dell'edizione

• Editore: Scitus Academics Llc
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 1681171880
• ISBN 13: 9781681171883
• Rilegatura: Copertina rigida
• Numero di pagine: 286
• Redattore: Chou Linsen
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile