Bøger i Advances in Mathematics serien

The theory of functional equations has been developed in a rapid and productive way in the second half of the Twentieth Century.

In semigroup theory there are certain kinds of band decompositions, which are useful in the study of the structure semigroups. This book focuses attention on such classes of semigroups and provides a systematic review on this subject. The first chapter is an introduction. The remaining chapters are devoted to special semigroup classes.

A complete and systematic introduction to the fundamentals of the hyperequational theory of universal algebra, offering the newest results on solid varieties of semirings and semigroups. The book aims to develop the theory of solid varieties as a system of mathematical discourse that is applicable in several concrete situations.

Natural duality theory is one of the major growth areas within general algebra. This combination of local simplicity and global complexity ensures that, for the study of natural duality theory, unary algebras are an excellent source of examples and counterexamples. A number of results appear here for the first time.

This detailed textbook presents a great deal of material on ordered sets not previously published in the still rather limited textbook literature. It should be suitable as a text for a course on order theory.

This book illustrates the basic ideas of regularity properties of functional equations by simple examples. It then treats most of the modern results about regularity of non-composite functional equations of several variables in a unified fashion.

The theory of functional equations has been developed in a rapid and productive way in the second half of the Twentieth Century.

In semigroup theory there are certain kinds of band decompositions, which are very useful in the study of the structure semigroups. There are a number of special semigroup classes in which these decompositions can be used very successfully. The book focuses attention on such classes of semigroups. Some of them are partially discussed in earlier books, but in the last thirty years new semigroup classes have appeared and a fairly large body of material has been published on them. The book provides a systematic review on this subject. The first chapter is an introduction. The remaining chapters are devoted to special semigroup classes. These are Putcha semigroups, commutative semigroups, weakly commutative semigroups, R-Commutative semigroups, conditionally commutative semigroups, RC-commutative semigroups, quasi commutative semigroups, medial semigroups, right commutative semigroups, externally commutative semigroups, E-m semigroups, WE-m semigroups, weakly exponential semigroups, (m,n)-commutative semigroups and n(2)-permutable semigroups. Audience: Students and researchers working in algebra and computer science.

This work presents new and old constructions of nearrings. Links between properties of the multiplicative of nearrings (as regularity conditions and identities) and the structure of nearrings are studied. Primality and minimality properties of ideals are collected. Some types of `simpler' nearrings are examined. Some nearrings of maps on a group are reviewed and linked with group-theoretical and geometrical questions. Audience: Researchers working in nearring theory, group theory, semigroup theory, designs, and translation planes. Some of the material will be accessible to graduate students.