A Guide to the Literature on Semirings and Their Applications in Mathematics and Information Sciences: With Complete Bibliography

ISBN-13: 9789048160600 / Angielski / Miękka / 2010 / 392 str.

K. Glazek

Opis

This book presents a guide to the extensive literature on the topic of semirings and includes a complete bibliography. It serves as a complement to the existing monographs and a point of reference to researchers and students on this topic. The literature on semirings has evolved over many years, in a variety of languages, by authors representing different schools of mathematics and working in various related fields. Recently, semiring theory has experienced rapid development, although publications are widely scattered. This survey also covers those newly emerged areas of semiring applications that have not received sufficient treatment in widely accessible monographs, as well as many lesser-known or forgotten' works.

The author has been collecting the bibliographic data for this book since 1985. Over the years, it has proved very useful for specialists. For example, J.S. Golan wrote he owed ... a special debt to Kazimierz Glazek, whose bibliography proved to be an invaluable guide to the bewildering maze of literature on semirings'. U. Hebisch and H.J. Weinert also mentioned his collection of literature had been of great assistance to them. Now updated to include publications up to the beginning of 2002, this work is available to a wide readership.

Audience: This volume is the first single reference that can guide the interested scholar or student to the relevant publications in semirings, semifields, algebraic theory of languages and automata, positive matrices and other generalisations, and ordered semigroups and groups.

Recenzje

From the reviews:

"The book deals with semirings (S, +, .) in the most inclusive sense ... . part one of the book presents on nearly 90 pages a short guide through the literature of different branches of semiring theory ... . In part two follows a (nearly) complete bibliography of semirings on about 290 pages. Finally, an excellent index is included which helps the reader to find very quickly the topic of interest and the relevant literature on it." (Udo Hebisch, Zentralblatt MATH, Vol. 1072 (23), 2005)

Spis treści

Preface. Part I: Short Guide to the Literature on Semirings. Introduction. 1. Preliminaries. 2. The Algebraic Theory of Semirings. 3. Linear Algebra Over Semirings. 4. Ordered Structures and Semirings. 5. Selected Applications of Semirings. Part II: Bibliography. Index.