This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.

Module theory over commutative asociative rings is usually extended to noncommutative associative rings by introducing the category of left (or right) modules. An alternative to this procedure is suggested by considering bimodules. A refined module theory for associative rings is used to investigate the bimodule structure of arbitary algebras and group actions on these algebras.

A filmmaker draws on the fields of neuroscience and evolutionary biology to focus on cinema’s visual nature. Cinematic analysis has often supported the notion that cinema can be understood by drawing parallels with language. Peter Wyeth contends that this analytical framework often fails to consider the fundamental fact of cinema’s visual nature. In The Matter of Vision, Wyeth seeks to redress this oversight by grounding his analysis in neuroscience and evolutionary biology, finding herein the potential for a qualitatively superior understanding of the cinematic medium.

Over the last few years, the study of complexes has become increasingly important. To date, however, most of the research is scattered throughout the literature or available only as lecture notes. Covers and Envelopes in the Category of Complexes of Modules collects these scattered notes and results into a single, concise volume that provides an account of recent developments in the theory and presents several new and important ideas. The author introduces the theory of complexes of modules using only elementary tools-making the field more accessible to non-specialists. He focuses the study on envelopes and covers in this category with respect to some well established and important classes of complexes. He places particular emphasis on DG-injective and DG-projective complexes and flat and DG-flat covers. Other topics covered include Zorn's Lemma for categories, preserving and reflecting covers by functors, orthogonality in the category of complexes, Gorenstein injective and projective complexes, and pure sequences of complexes. Along with its value as a collection of recent work in the field, Covers and Envelopes in the Category of Complexes of Modules presents powerful new ideas that will undoubtedly advance homological methods. Mathematicians-especially researchers in module theory and homological algebra-will welcome this volume as a reference guide and for its new and important results.

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With the dramatic increase in RNA 3D structure determination in recent years, we now know that RNA molecules are highly structured. Moreover, knowledge of RNA 3D structures has proven crucial for understanding in atomic detail how they carry out their biological functions. Because of the huge number of potentially important RNA molecules in biology, many more than can be studied experimentally, we need theoretical approaches for predicting 3D structures on the basis of sequences alone. This volume provides a comprehensive overview of current progress in the field by leading practitioners employing a variety of methods to model RNA 3D structures by homology, by fragment assembly, and by de novo energy and knowledge-based approaches.

This book is about interpretation as it pertains to literature, philosophy, and psychoanalysis. It argues against certain trends of thought that claim we should do without interpretation by demonstrating that interpretation, as described by psychoanalysis, is already a fundamental aspect of all human experience. Egginton examines the idea of interpretation developed by Freud; how that notion was in turn changed by Lacan; the debate around psychoanalytic interpretation staged by philosophers like Deleuze and Derrida; and finally how a psychoanalytic notion of interpretation is necessary for even the most basic experience of consciousness.

"In this book, modules over a specific class of rings, the discrete valuations domains, are considered. Such modules call for a special consideration, since they have specific properties and play an important role in various areas of algebra, especially of commutative algebra. The text is accompanied by exercises, historical remarks, links to related fields and open problems. It is useful for students, graduates studying algebra, young researchers, and experts."--BOOK JACKET.

Contains the proceedings of an international conference on abelian groups and modules held recently in Colorado Springs. Presents the latest developments in abelian groups that have facilitated cross-fertilization of new techniques from diverse areas such as the representation theory of posets, model theory, set theory, and module theory.

The theory of rings of quotients has its origin in the work of (j). Ore and K. Asano on the construction of the total ring of fractions, in the 1930's and 40's. But the subject did not really develop until the end of the 1950's, when a number of important papers appeared (by R. E. Johnson, Y. Utumi, A. W. Goldie, P. Gabriel, J. Lambek, and others). Since then the progress has been rapid, and the subject has by now attained a stage of maturity, where it is possible to make a systematic account of it (which is the purpose of this book). The most immediate example of a ring of quotients is the field of fractions Q of a commutative integral domain A. It may be characterized by the two properties: (i) For every qEQ there exists a non-zero SEA such that qSEA. (ii) Q is the maximal over-ring of A satisfying condition (i). The well-known construction of Q can be immediately extended to the case when A is an arbitrary commutative ring and S is a multiplicatively closed set of non-zero-divisors of A. In that case one defines the ring of fractions Q = A [S-l] as consisting of pairs (a, s) with aEA and SES, with the declaration that (a, s)=(b, t) if there exists UES such that uta = usb. The resulting ring Q satisfies (i), with the extra requirement that SES, and (ii).