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Galois Connections and Applications
Galois connections provide the order- or structure-preserving passage between two worlds of our imagination - and thus are inherent in hu man thinking wherever logical or mathematical reasoning about cer tain hierarchical structures is involved. Order-theoretically, a Galois connection is given simply by two opposite order-inverting (or order preserving) maps whose composition yields two closure operations (or one closure and one kernel operation in the order-preserving case). Thus, the "hierarchies" in the two opposite worlds are reversed or transported when passing to the other world, and going forth and back becomes a stationary process when iterated. The advantage of such an "adjoint sit...
The Novellino or One Hundred Ancient Tales
First published in 1997. Considered one of the first prose works in Italian and a precursor of the Decameron,this is the first complete translation of the Novellino into English, based on the 1525 editio princeps. While manuscripts vary as to wording and the number of tales, the 1525 first edition follows seven of the eight known manuscripts closely. The text includes a transcription of the 1525 edition, taken from the copy in the Parma Biblioteca Palatina. This transcription has been altered as little as possible, diacriticals are added and capitalization is systematized, but no attempt has been made to modernize the language. Vocabulary notes are provided, as are ample notes to explain the historical and cultural significance of figures and events in the tales. There is one bibliography for the Novellino and another for the explanatory notes.
Grbner Bases in Ring Theory
This monograph strives to introduce a solid foundation on the usage of Grbner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. It also reveals the intrinsic structural properties of Grbner bases, presents a constructive PBW theory in a quite extensive context and, along the routes built via the PBW theory, the book demonstrates novel methods of using Grbner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand?Kirillov dimension, Noetherianity, (semi-)primeness, PI-property, finiteness of global homological dimension, Hilbert series, (non-)homogeneous p-Koszulity, PBW-deformation...
Monoids, Acts and Categories
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, Univ...
Combinatorics And Graph Theory - Proceedings Of The Spring School And International Conference On Combinatorics
This volume contains selected papers presented at the Spring School and International Conference on Combinatorics. Topics discussed include: Enumeration, Design, Graphs, Hypergraphs and Combinatorial Optimization, etc. Covering a broad range, this book should appeal to a wide spectrum of researchers in combinatorics and graph theory.
Topological Rings Satisfying Compactness Conditions
Introduction In the last few years a few monographs dedicated to the theory of topolog ical rings have appeared [Warn27], [Warn26], [Wies 19], [Wies 20], [ArnGM]. Ring theory can be viewed as a particular case of Z-algebras. Many general results true for rings can be extended to algebras over commutative rings. In topological algebra the structure theory for two classes of topological algebras is well developed: Banach algebras; and locally compact rings. The theory of Banach algebras uses results of Banach spaces, and the theory of locally compact rings uses the theory of LCA groups. As far as the author knows, the first papers on the theory of locally compact rings were [Pontr1]' [J1], [J2], [JT], [An], lOt], [K1]' [K2]' [K3], [K4], [K5], [K6]. Later two papers, [GS1,GS2]appeared, which contain many results concerning locally compact rings. This book can be used in two w.ays. It contains all necessary elementary results from the theory of topological groups and rings. In order to read these parts of the book the reader needs to know only elementary facts from the theories of groups, rings, modules, topology. The book consists of two parts.
