Semigroups

Fülszöveg

The aim of this book was to combine some of the authors', their scholars' and other, researchers' work in the area of semigroups in a unified presentation with an emphasis on finite semigroups.
The focus of this volume is on a classification of the elements of semigroups according to their induced translations and the decomposition of semigroups according to this classification.
The problem of decomposing can be approached in different ways depending on the operations on which the decomposition is based:
1. Products: The powerful Krohn-Rhodes theory.
2. Unions: A decomposition theory for semigroups can also be based on the operation of union instead of product. In this case a semigroup is considered as a union of a family of subsets where the index set and the subsets satisfy certain structural constraints.
In this book a certain kind of union-based decompositions is considered: "5-decompositions". Semigroups are represented as partial semigroups of disjoint subsemigroups... Tovább

Fülszöveg

The aim of this book was to combine some of the authors', their scholars' and other, researchers' work in the area of semigroups in a unified presentation with an emphasis on finite semigroups.
The focus of this volume is on a classification of the elements of semigroups according to their induced translations and the decomposition of semigroups according to this classification.
The problem of decomposing can be approached in different ways depending on the operations on which the decomposition is based:
1. Products: The powerful Krohn-Rhodes theory.
2. Unions: A decomposition theory for semigroups can also be based on the operation of union instead of product. In this case a semigroup is considered as a union of a family of subsets where the index set and the subsets satisfy certain structural constraints.
In this book a certain kind of union-based decompositions is considered: "5-decompositions". Semigroups are represented as partial semigroups of disjoint subsemigroups according to a classification of elements.
This volume does not attempt to provide a "complete" presentation of semigroup theory. Instead, we focus on essentially one aspect: the classification of elements by properties of the induced translation and the related global structural properties of a semigroup. Several new results were found in particular, on increasing elements in semigroups and many new open problems were identified. In this sense, we hope that this book may serve not only as a summary but also a starting point for further research. Vissza