03437nam a22005175i 4500 978-981-99-8285-1 DE-He213 20251030111451.0 cr nn 008mamaa 240228s2024 si | s |||| 0|eng d 9789819982851 978-981-99-8285-1 10.1007/978-981-99-8285-1 doi QA251.5 PBF bicssc MAT002010 bisacsh PBF thema Chen, Jianlong. author. aut http://id.loc.gov/vocabulary/relators/aut 72026 Algebraic Theory of Generalized Inverses [electronic resource] / by Jianlong Chen, Xiaoxiang Zhang. 1st ed. 2024. Singapore : Springer Nature Singapore : Imprint: Springer, 2024. XI, 322 p. 1 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Preface -- Algebraic Basic Knowledge -- Moore-Penrose Inverses -- Group Inverses -- Drazin Inverses -- Core Inverses -- Pseudo Core Inverses -- Bibliography -- Index. 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 generalized inverses 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. Associative rings. 72027 Associative algebras. 72028 Group theory. 70149 Associative Rings and Algebras. 72029 Group Theory and Generalizations. 70154 Zhang, Xiaoxiang. author. aut http://id.loc.gov/vocabulary/relators/aut 72030 SpringerLink (Online service) Springer Nature eBook Printed edition: 9789819982844 Printed edition: 9789819982868 Printed edition: 9789819982875 https://doi.org/10.1007/978-981-99-8285-1 ZDB-2-SMA ZDB-2-SXMS 57977 57977