Theory of generalized inverses over commutative rings

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Theory of generalized inverses over commutative rings / K.P.S. Bhaskara Rao

資料種別:: 図書
出版情報:: London : Taylor and Francis, c2002
形態:: xi, 167 p. ; 24 cm
シリーズ名:: Algebra, logic and applications series ; 17 <BA0740816X>
著者名:: Bhaskara Rao, K. P. S. <DA01725246>
ISBN:: 9780415272483 [0415272483]
書誌ID:: BA56759320

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注記:

Bibliography: p. 153-165
Includes index

言語:

英語

目次情報:

Elementary Results on Rings

Foreword

Matrix Algebra Over Rings

Regular Elements in a Ring

Preface

Regularity - Principal Ideal Rings

Regularity - Basics / 1：

Regularity - Integral Domains

Elementary results on rings

Regularity - Commutative Rings

Special Topics / 2：

Matrix algebra over rings

Elementary notions / 2.1：

Determinants / 2.2：

The [partial differential]/[partial differential]a[subscript ij] notation / 2.3：

Rank of a matrix / 2.4：

Compound matrices / 2.5：

Regular elements in a ring / 3：

The Moore-Penrose equations / 3.1：

Regular elements and regular matrices / 3.2：

A Theorem of Von Neumann / 3.3：

Inverses of matrices / 3.4：

M-P inverses / 3.5：

Regularity - principal ideal rings / 4：

Some results on principal ideal rings / 4.1：

Smith Normal Form Theorem / 4.2：

Regular matrices over Principal Ideal Rings / 4.3：

An algorithm for Euclidean domains / 4.4：

Reflexive g-inverses of matrices / 4.5：

Some special integral domains / 4.6：

Examples / 4.7：

Regularity - basics / 5：

Regularity of rank one matrices / 5.1：

A basic result on regularity / 5.2：

A result of Prasad and Robinson / 5.3：

Regularity - integral domains / 6：

Regularity of matrices / 6.1：

All reflexive g-inverses / 6.2：

M-P inverses over integral domains / 6.3：

Generalized inverses of the form PCQ / 6.4：

{1,2,3}- and {1,2,4}-inverses / 6.5：

Group inverses over integral domains / 6.6：

Drazin inverses over integral domains / 6.7：

Regularity - commutative rings / 7：

Commutative rings with zero divisors / 7.1：

Rank one matrices / 7.2：

Rao-regular matrices / 7.3：

Regular matrices over commutative rings / 7.4：

All generalized inverses / 7.5：

M-P inverses over commutative rings / 7.6：

Group inverses over commutative rings / 7.7：

Drazin inverses over commutative rings / 7.8：

Special topics / 8：

Generalized Cramer Rule / 8.1：

A rank condition for consistency / 8.2：

Minors of reflexive g-inverses / 8.3：

Bordering of regular matrices / 8.4：

Regularity over Banach algebras / 8.5：

Group inverses in a ring / 8.6：

M-P inverses in a ring / 8.7：

Group inverse of the companion matrix / 8.8：

Bibliography

Index

Elementary Results on Rings

Foreword

Matrix Algebra Over Rings

Regular Elements in a Ring

Preface

Regularity - Principal Ideal Rings

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