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010   $a981-9982-85-5
024 7 $a10.1007/978-981-99-8285-1
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035   $a(DE-He213)978-981-99-8285-1
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100   $a20240228d2024      u|         0
101 0 $aeng
135   $aur|||||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aAlgebraic Theory of Generalized Inverses /$fby Jianlong Chen, Xiaoxiang Zhang
205   $a1st ed. 2024.
210  1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2024.
215   $a1 online resource (331 pages)
311 08$a981-9982-84-7 
320   $aIncludes bibliographical references and index.
327   $aPreface -- Algebraic Basic Knowledge -- Moore-Penrose Inverses -- Group Inverses -- Drazin Inverses -- Core Inverses -- Pseudo Core Inverses -- Bibliography -- Index.
330   $aMost 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.
606   $aAssociative rings
606   $aAssociative algebras
606   $aGroup theory
606   $aAssociative Rings and Algebras
606   $aGroup Theory and Generalizations
615  0$aAssociative rings.
615  0$aAssociative algebras.
615  0$aGroup theory.
615 14$aAssociative Rings and Algebras.
615 24$aGroup Theory and Generalizations.
676   $a512.5
700   $aChen$b Jianlong$01732568
702   $aZhang$b Xiaoxiang
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910842288803321
996   $aAlgebraic Theory of Generalized Inverses$94146938
997   $aUNINA