Buch, Englisch, 213 Seiten, Format (B × H): 155 mm x 235 mm
Buch, Englisch, 213 Seiten, Format (B × H): 155 mm x 235 mm
Reihe: Springer Asia Pacific Mathematics Series
ISBN: 978-981-9273-42-3
Verlag: Springer Nature Singapore
This book describes the cross-connection theory of Grillet and Nambooripad in the context of regular semigroups as a relation connecting the category of principal left ideals and the category of principal right ideals. Category theory has been widely used nowadays to provide unified structure to analyse various aspects of a phenomenon. A category can be viewed as a system behaving like a collection of sets and mappings between the member sets. In the category terminology, these collections are named as objects and morphisms. When the class of objects of a category is a set rather than a proper class, the category is said to be a small category. Small categories can be realized to have a structure which is a generalization of the structure of a group, regular semigroup, or groupoid. More precisely we can regard a small category as a set with an associative partial binary operation admitting relative identities. Here relative identity means identity relative to each element. Normal categories have been introduced in the context of describing structure of regular semigroups based on the relations on ideals. This structure theory is known as cross connection theory. The concept of cross connection was introduced by Grillet (1974) to describe the relation connecting the partially ordered set of Green’s R-classes Green’s L-classes of a regular semigroup. In Nambooripad's generalization the category of principal left ideals and that of principal right ideals have been abstracted to the concept of normal categories. In recent years, normal categories have been studied extensively and several publications relating to various aspects of normal categories have appeared. Structure theory of regular semigroups and regular rings has been described for various special classes of semigroups and rings.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Preliminaries.- Normal Categories.- Normal Category L(S).- Semigroup of Normal Cones.- The Normal Dual.- Cross Connections.- Cross Connection Semigroup.- Compatible categories.- Unit Regular Semigroups.
