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＜電子ブック＞
Noetherian Semigroup Algebras / by Eric Jespers, Jan Okninski
(Algebra and Applications. ISSN:21922950 ; 7)

版	1st ed. 2007.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2007
本文言語	英語
大きさ	X, 364 p : online resource
著者標目	*Jespers, Eric author Okninski, Jan author SpringerLink (Online service)
件　名	LCSH:Group theory LCSH:Associative rings LCSH:Associative algebras FREE:Group Theory and Generalizations FREE:Associative Rings and Algebras
一般注記	Prerequisites on semigroup theory -- Prerequisites on ring theory -- Algebras of submonoids of polycyclic-by-finite groups -- General Noetherian semigroup algebras -- Principal ideal rings -- Maximal orders and Noetherian semigroup algebras -- Monoids of I-type -- Monoids of skew type -- Examples Within the last decade, semigroup theoretical methods have occurred naturally in many aspects of ring theory, algebraic combinatorics, representation theory and their applications. In particular, motivated by noncommutative geometry and the theory of quantum groups, there is a growing interest in the class of semigroup algebras and their deformations. This work presents a comprehensive treatment of the main results and methods of the theory of Noetherian semigroup algebras. These general results are then applied and illustrated in the context of important classes of algebras that arise in a variety of areas and have been recently intensively studied. Several concrete constructions are described in full detail, in particular intriguing classes of quadratic algebras and algebras related to group rings of polycyclic-by-finite groups. These give new classes of Noetherian algebras of small Gelfand-Kirillov dimension. The focus is on the interplay between their combinatorics and the algebraic structure. This yields a rich resource of examples that are of interest not only for the noncommutative ring theorists, but also for researchers in semigroup theory and certain aspects of group and group ring theory. Mathematical physicists will find this work of interest owing to the attention given to applications to the Yang-Baxter equation HTTP:URL=https://doi.org/10.1007/1-4020-5810-1

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