Modes

Modes
Author: Anna B. Romanowska
Publisher: World Scientific
Total Pages: 640
Release: 2002
Genre: Science
ISBN: 9789810249427

Introduces the theory and application of modes, covering topics in universal algebra, category theory, and modal theory, and includes exercises to illustrate concepts.

Universal Algebra and Applications in Theoretical Computer Science

Universal Algebra and Applications in Theoretical Computer Science
Author: Klaus Denecke
Publisher: CRC Press
Total Pages: 400
Release: 2002-01-18
Genre: Mathematics
ISBN: 9781584882541

Over the past 20 years, the emergence of clone theory, hyperequational theory, commutator theory and tame congruence theory has led to a growth of universal algebra both in richness and in applications, especially in computer science. Yet most of the classic books on the subject are long out of print and, to date, no other book has integrated these theories with the long-established work that supports them. Universal Algebra and Applications in Theoretical Computer Science introduces the basic concepts of universal algebra and surveys some of the newer developments in the field. The first half of the book provides a solid grounding in the core material. A leisurely pace, careful exposition, numerous examples, and exercises combine to form an introduction to the subject ideal for beginning graduate students or researchers from other areas. The second half of the book focuses on applications in theoretical computer science and advanced topics, including Mal'cev conditions, tame congruence theory, clones, and commutators. The impact of the advances in universal algebra on computer science is just beginning to be realized, and the field will undoubtedly continue to grow and mature. Universal Algebra and Applications in Theoretical Computer Science forms an outstanding text and offers a unique opportunity to build the foundation needed for further developments in its theory and in its computer science applications.

A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences

A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences
Author: K. Glazek
Publisher: Springer Science & Business Media
Total Pages: 394
Release: 2013-06-29
Genre: Mathematics
ISBN: 9401599645

This volume presents a short guide to the extensive literature concerning semir ings along with a complete bibliography. The literature has been created over many years, in variety of languages, by authors representing different schools of mathematics and working in various related fields. In many instances the terminology used is not universal, which further compounds the difficulty of locating pertinent sources even in this age of the Internet and electronic dis semination of research results. So far there has been no single reference that could guide the interested scholar or student to the relevant publications. This book is an attempt to fill this gap. My interest in the theory of semirings began in the early sixties, when to gether with Bogdan W ~glorz I tried to investigate some algebraic aspects of compactifications of topological spaces, semirings of semicontinuous functions, and the general ideal theory for special semirings. (Unfortunately, local alge braists in Poland told me at that time that there was nothing interesting in investigating semiring theory because ring theory was still being developed). However, some time later we became aware of some similar investigations hav ing already been done. The theory of semirings has remained "my first love" ever since, and I have been interested in the results in this field that have been appearing in literature (even though I have not been active in this area myself).

An Introduction to Quasigroups and Their Representations

An Introduction to Quasigroups and Their Representations
Author: Jonathan D. H. Smith
Publisher: CRC Press
Total Pages: 353
Release: 2006-11-15
Genre: Mathematics
ISBN: 1420010638

Collecting results scattered throughout the literature into one source, An Introduction to Quasigroups and Their Representations shows how representation theories for groups are capable of extending to general quasigroups and illustrates the added depth and richness that result from this extension. To fully understand representation theory,