Algebraic Theory of Generalized Inverses

Jianlong Chen

ISBN 10: 9819982871 / ISBN 13: 9789819982875

Published by Springer, Springer, 2025

About this Item

Druck auf Anfrage Neuware - Printed after ordering - Most of the existing monographs on generalized inverses are based on linear algebra tools and geometric methods of Banach (Hilbert) spaces to introduce generalized inverses of complex matrices and operators and their related applications, or focus on generalized inverses of matrices over special rings like division rings and integral domains, and does not include the results in general algebraic structures such as arbitrary rings, semigroups and categories, which are precisely the most general cases.In this book, five important generalized inverses are introduced in these algebraic structures. Moreover, noting that the (pseudo) core inverse was introduced in the last decade and has attracted much attention, this book also covers the very rich research results on it, so as to be a necessary supplement to the existing monographs. This book starts with decompositions of matrices, introduces the basic properties of generalized inverses of matrices, and then discusses generalizedinverses of elements in rings and semigroups, as well as morphisms in categories. The algebraic nature of generalized inverses is presented, and the behavior of generalized inverses are related to the properties of the algebraic system.Scholars and graduate students working on the theory of rings, semigroups and generalized inverses of matrices and operators will find this book helpful.

Seller Inventory # 9789819982875

Bibliographic Details

• Title: Algebraic Theory of Generalized Inverses
• Publisher: Springer, Springer
• Publication Date: 2025
• Language: English
• ISBN 10: 9819982871
• ISBN 13: 9789819982875
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 19D millimeters 235 millimeters width by 155 millimeters height by 19 millimeters depth
• Weight: 511 grams

About this title

Synopsis

Most of the existing monographs on generalized inverses are based on linear algebra tools and geometric methods of Banach (Hilbert) spaces to introduce generalized inverses of complex matrices and operators and their related applications, or focus on generalized inverses of matrices over special rings like division rings and integral domains, and does not include the results in general algebraic structures such as arbitrary rings, semigroups and categories, which are precisely the most general cases.

In this book, five important generalized inverses are introduced in these algebraic structures. Moreover, noting that the (pseudo) core inverse was introduced in the last decade and has attracted much attention, this book also covers the very rich research results on it, so as to be a necessary supplement to the existing monographs. This book starts with decompositions of matrices, introduces the basic properties of generalized inverses of matrices, and then discusses generalizedinverses of elements in rings and semigroups, as well as morphisms in categories. The algebraic nature of generalized inverses is presented, and the behavior of generalized inverses are related to the properties of the algebraic system.

Scholars and graduate students working on the theory of rings, semigroups and generalized inverses of matrices and operators will find this book helpful.

About the Author

Jianlong Chen is a Professor at School of Mathematics, Southeast University. He is engaged in research in algebra, including ring theory, module theory, homological theory, matrix theory and generalized inverse theory.

Xiaoxiang Zhang is a Professor at School of Mathematics, Southeast University. He is engaged in research in algebra, with research interests including the theory of rings, modules, generalized inverses and homological algebra.