S. K. Jain – författare

This unique and comprehensive volume provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a homological property. The finiteness conditions and homological properties are closely interrelated in the sense that either hypothesis induces the other in some form. This is the first book to bring all of this important material on the subjecttogether.Over the last 25 years or more numerous mathematicians have investigated rings whose factor rings or factor modules have a finiteness condition or a homological property. They made important contributions leading to new directions and questions, which are listed at the end of each chapter for the benefit of future researchers. There is a wealth of material on the topic which is combined in this book, it contains more than 200 references and is not claimed to be exhaustive.This book will appeal to graduate students, researchers, and professionals in algebra with a knowledge of basic noncommutative ring theory, as well as module theory and homological algebra, equivalent to a one-year graduate course in the theory of rings and modules.

Geomicrobiology is a combination of geology and microbiology, and includes the study of interaction of microorganisms with their environment, such as in sedimentary rocks. This is a new and rapidly-developing field that has led in the past decade to a radically-revised view of the diversity and activity of microbial life on Earth. Geomicrobiology examines the role that microbes have played in the past and are currently playing in a number of fundamental geological processes. The present book is of great importance for researchers working in the field of microbiology, biotechnology, geology and environmental biotechnology. It can be a major reference book for students as well as researchers.

This book represents a complete course in abstract algebra, providing instructors with flexibility in the selection of topics to be taught in individual classes. All the topics presented are discussed in a direct and detailed manner. Throughout the text, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. The book contains many examples fully worked out and a variety of problems for practice and challenge. Solutions to the odd-numbered problems are provided at the end of the book. This new edition contains an introduction to lattices, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Lasker-Noether theorem. In addition, there are over 100 new problems and examples, particularly aimed at relating abstract concepts to concrete situations.

This book represents a complete course in abstract algebra, providing instructors with flexibility in the selection of topics to be taught in individual classes. All the topics presented are discussed in a direct and detailed manner. Throughout the text, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. The book contains many examples fully worked out and a variety of problems for practice and challenge. Solutions to the odd-numbered problems are provided at the end of the book. This new edition contains an introduction to lattices, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Lasker-Noether theorem. In addition, there are over 100 new problems and examples, particularly aimed at relating abstract concepts to concrete situations.

Presenting current developments and trends in ring theory, this text highlights newer techniques as well as those that are more established.

Geomicrobiology is a combination of geology and microbiology, and includes the study of interaction of microorganisms with their environment, such as in sedimentary rocks. This is a new and rapidly-developing field that has led in the past decade to a radically-revised view of the diversity and activity of microbial life on Earth. Geomicrobiology e

This volume contains the proceedings of the Virtual Conference on Noncommutative Rings and their Applications VII, in honor of Tariq Rizvi, held from July 5-7, 2021, and the Virtual Conference on Quadratic Forms, Rings and Codes, held on July 8, 2021, both of which were hosted by the Universite d'Artois, Lens, France.The articles cover topics in commutative and noncommutative algebra and applications to coding theory. In some papers, applications of Frobenius rings, the skew group rings, and iterated Ore extensions to coding theory are discussed. Other papers discuss classical topics, such as Utumi rings, Baer rings, nil and nilpotent algebras, and Brauer groups. Still other articles are devoted to various aspects of the elementwise study for rings and modules. Lastly, this volume includes papers dealing with questions in homological algebra and lattice theory. The articles in this volume show the vivacity of the research of noncommutative rings and its influence on other subjects.

Geomicrobiology is a combination of geology and microbiology, and includes the study of interaction of microorganisms with their environment, such as in sedimentary rocks. This is a new and rapidly-developing field that has led in the past decade to a radically-revised view of the diversity and activity of microbial life on Earth. Geomicrobiology examines the role that microbes have played in the past and are currently playing in a number of fundamental geological processes. The present book is of great importance for researchers working in the field of microbiology, biotechnology, geology and environmental biotechnology. It can be a major reference book for students as well as researchers.

Rye first appeared rather late in the history of human civilization. The oldest archaeological records of rye date from the Hallstatt period in Silesia, Thuringia and Westfalia and from the Lacene period. After the pioneering work of N. 1. V AVILOV on the origin of cultivated plants three broad classes came in recognition: wild, weedy and cultivated rye. As a crop, rye is most winterhardy of all cereals so that in Northern Europe its cultivation reaches beyond the Arctic circle in Finland. While Soviet Russia contributes most to the total world production, in Finland, Poland, Germany, Sweden, Netherlands and Belgium also its rank is high among grain crops. It is striking to note that for the past many years, research on practical agronomical and breeding problems has been quite active in these countries and current­ ly attempts to improve rye are being made on modern lines. Some of the main problems in this field concern with the development of hybrid varieties, improvement of autotetraploid fertility, use of best pollina­ tion procedures to obtain highly self-fertile lines and the transfer of rye characters to wheat as such or in the form of amphiploid Triticales. In Russia, however, the Michurinist agrobiologists are primarily engaged in the study of interspecific conversions, branched ear types and nutritional methods of improving varieties, and perhaps this is one reason of only little having been known about rye genetics.

or fruit production as a consequence of the lack of optimum pollination conditions (CLARK and FRYER, 1920; ARMSTRONG and WHITE, 1935; VALLEAU, 1918; KVAALE, 1927; and many others). In order to mini­ mize the influence of poor pollen producers, systematic planning of a field planting or an orchard might be necessary. Above all, the im­ portant reason for its wide popularity is its potential use in the com­ mercial production of hybrid seed. A male-sterile plant is an effective female for a crossing program and its employment renders the labori­ ous procedure of emasculation superfluous. ]ONES and EMSWELLER (1937) and STEPHENS (1937) were probably the first to outline a scheme of its application in onion and sorghum respectively. However certain specific problems have limited the practicability and hence some of them will be mentioned in a later seetion (Section VIII). Lately several attempts have been made to obtain some chemie al method for the artificial induction of male sterility. However, for a successful approach to the induction problem a thorough understan­ ding of various pathways that bring about pollen abortion in naturally occurring cases, would be of great value. It may be hoped that data from these induction experiments alongwith the available biochemi­ cal analyses would lead to the emergence and elucidation of useful information of both theoretical and practical interest.

Rye first appeared rather late in the history of human civilization. The oldest archaeological records of rye date from the Hallstatt period in Silesia, Thuringia and Westfalia and from the Lacene period. After the pioneering work of N. 1. V AVILOV on the origin of cultivated plants three broad classes came in recognition: wild, weedy and cultivated rye. As a crop, rye is most winterhardy of all cereals so that in Northern Europe its cultivation reaches beyond the Arctic circle in Finland. While Soviet Russia contributes most to the total world production, in Finland, Poland, Germany, Sweden, Netherlands and Belgium also its rank is high among grain crops. It is striking to note that for the past many years, research on practical agronomical and breeding problems has been quite active in these countries and current­ ly attempts to improve rye are being made on modern lines. Some of the main problems in this field concern with the development of hybrid varieties, improvement of autotetraploid fertility, use of best pollina­ tion procedures to obtain highly self-fertile lines and the transfer of rye characters to wheat as such or in the form of amphiploid Triticales. In Russia, however, the Michurinist agrobiologists are primarily engaged in the study of interspecific conversions, branched ear types and nutritional methods of improving varieties, and perhaps this is one reason of only little having been known about rye genetics.

or fruit production as a consequence of the lack of optimum pollination conditions (CLARK and FRYER, 1920; ARMSTRONG and WHITE, 1935; VALLEAU, 1918; KVAALE, 1927; and many others). In order to mini­ mize the influence of poor pollen producers, systematic planning of a field planting or an orchard might be necessary. Above all, the im­ portant reason for its wide popularity is its potential use in the com­ mercial production of hybrid seed. A male-sterile plant is an effective female for a crossing program and its employment renders the labori­ ous procedure of emasculation superfluous. ]ONES and EMSWELLER (1937) and STEPHENS (1937) were probably the first to outline a scheme of its application in onion and sorghum respectively. However certain specific problems have limited the practicability and hence some of them will be mentioned in a later seetion (Section VIII). Lately several attempts have been made to obtain some chemie al method for the artificial induction of male sterility. However, for a successful approach to the induction problem a thorough understan­ ding of various pathways that bring about pollen abortion in naturally occurring cases, would be of great value. It may be hoped that data from these induction experiments alongwith the available biochemi­ cal analyses would lead to the emergence and elucidation of useful information of both theoretical and practical interest.

This volume consists of a collection of invited papers on the theory of rings and modules, most of which were presented at the biennial Ohio State — Denison Conference, May 1992, in memory of Hans Zassenhaus. The topics of these papers represent many modern trends in Ring Theory. The wide variety of methodologies and techniques demonstrated will be valuable in particular to young researchers in the area. Covering a broad range, this book should appeal to a wide spectrum of researchers in algebra and number theory.

The volume contains selected articles presented in the ZOOM conference on History of Mathematics in Jain Literature, December 2020, and also contains articles invited by the editors on specific topics.The main objective for the conference was to bring to the attention of historians in mathematics that there is a plenty of literature written by monks and scholars in Jaina literature that contains elements of arithmetic, algebra and geometry, independent of discoveries by other cultures in the past. The talks and the discussions at the conference highlighted a need for a volume that can be recommended as a reference book for a course on History of Mathematics in the Departments of Mathematics and Education in colleges and universities. This is our hope that the present volume would fill up the gap on the lack of knowledge of past Jaina contributions.

This book discusses the revolution of cycles and rhythms that is expected to take place in different branches of science and engineering in the 21st century, with a focus on communication and information processing. It presents high-quality papers in vibration sciences, rhythms and oscillations, neurosciences, mathematical sciences, and communication. It includes major topics in engineering and structural mechanics, computer sciences, biophysics and biomathematics, as well as other related fields. Offering valuable insights, it also inspires researchers to work in these fields. The papers included in this book were presented at the 1st International Conference on Engineering Vibration, Communication and Information Processing (ICoEVCI-2018), India.

This book discusses the revolution of cycles and rhythms that is expected to take place in different branches of science and engineering in the 21st century, with a focus on communication and information processing. It presents high-quality papers in vibration sciences, rhythms and oscillations, neurosciences, mathematical sciences, and communication. It includes major topics in engineering and structural mechanics, computer sciences, biophysics and biomathematics, as well as other related fields. Offering valuable insights, it also inspires researchers to work in these fields. The papers included in this book were presented at the 1st International Conference on Engineering Vibration, Communication and Information Processing (ICoEVCI-2018), India.

This book comprises select proceedings of the International Conference on Trends and Recent Advances in Civil Engineering (TRACE 2022). It discusses the latest topics related to energy and environmental engineering. The topics covered include green and clean technologies, zero-energy buildings, solar energy, energy conservation and heat recovery, solar architecture, artificial intelligence for sustainable buildings, climate change, and plastic and air pollution. This book is useful for researchers and professionals working in the area of civil engineering and energy and environmental engineering.

This book comprises select proceedings of the International Conference on Trends and Recent Advances in Civil Engineering (TRACE 2022). It discusses the latest topics related to energy and environmental engineering. The topics covered include green and clean technologies, zero-energy buildings, solar energy, energy conservation and heat recovery, solar architecture, artificial intelligence for sustainable buildings, climate change, and plastic and air pollution. This book is useful for researchers and professionals working in the area of civil engineering and energy and environmental engineering.