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• catalog abstract "Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. Their study has attracted many prominent researchers and has motivated the creation of theories which may now be considered part of general commutative ring theory. The book gives a first coherent treatment of the structure of determinantal rings. The main approach is via the theory of algebras with straightening law. This approach suggest (and is simplified by) the simultaneous treatment of the Schubert subvarieties of Grassmannian. Other methods have not been neglected, however. Principal radical systems are discussed in detail, and one section is devoted to each of invariant and representation theory. While the book is primarily a research monograph, it serves also as a reference source and the reader requires only the basics of commutative algebra together with some supplementary material found in the appendix. The text may be useful for seminars following a course in commutative ring theory since a vast number of notions, results, and techniques can be illustrated significantly by applying them to determinantal rings.".
• catalog contributor b2195426.
• catalog contributor b2195427.
• catalog created "c1988.".
• catalog date "1988".
• catalog date "c1988.".
• catalog dateCopyrighted "c1988.".
• catalog description "Bibliography: p. [219]-228.".
• catalog description "Contents: Preliminaries -- Ideals of Maximal Minors -- Generically Perfect Ideals -- Algebras with Straightening Law on Posets of Minors -- The Structure of an ASL -- Integrity and Normality. The Singular Locus -- Generic Points and Invariant Theory -- The Divisor Class Group and the Canonical Class -- Powers of Ideals of Maximal Minors -- Primary Decomposition -- Representation Theory -- Principal Radical Systems -- Generic Modules -- The Module of Kähler Differentials -- Derivations and Rigidity -- Appendix -- Bibliography -- Index of Notations -- Subject Index.".
• catalog description "Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. Their study has attracted many prominent researchers and has motivated the creation of theories which may now be considered part of general commutative ring theory. The book gives a first coherent treatment of the structure of determinantal rings. The main approach is via the theory of algebras with straightening law. This approach suggest (and is simplified by) the simultaneous treatment of the Schubert subvarieties of Grassmannian. Other methods have not been neglected, however. Principal radical systems are discussed in detail, and one section is devoted to each of invariant and representation theory. While the book is primarily a research monograph, it serves also as a reference source and the reader requires only the basics of commutative algebra together with some supplementary material found in the appendix. The text may be useful for seminars following a course in commutative ring theory since a vast number of notions, results, and techniques can be illustrated significantly by applying them to determinantal rings.".
• catalog extent "vii, 236 p. :".
• catalog hasFormat "Determinantal rings.".
• catalog identifier "0387194681 (pbk.)".
• catalog identifier "3540194681".
• catalog isFormatOf "Determinantal rings.".
• catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1327.".
• catalog isPartOf "Lecture notes in mathematics ; 1327".
• catalog issued "1988".
• catalog issued "c1988.".
• catalog language "eng".
• catalog publisher "Berlin ; New York : Springer-Verlag,".
• catalog relation "Determinantal rings.".
• catalog subject "510 s 512/.4 19".
• catalog subject "Determinantal rings.".
• catalog subject "Group theory.".
• catalog subject "Mathematics.".
• catalog subject "QA3 .L28 no. 1327 QA251.3".
• catalog subject "Topological Groups.".
• catalog tableOfContents "Contents: Preliminaries -- Ideals of Maximal Minors -- Generically Perfect Ideals -- Algebras with Straightening Law on Posets of Minors -- The Structure of an ASL -- Integrity and Normality. The Singular Locus -- Generic Points and Invariant Theory -- The Divisor Class Group and the Canonical Class -- Powers of Ideals of Maximal Minors -- Primary Decomposition -- Representation Theory -- Principal Radical Systems -- Generic Modules -- The Module of Kähler Differentials -- Derivations and Rigidity -- Appendix -- Bibliography -- Index of Notations -- Subject Index.".
• catalog title "Determinantal rings / Winfried Bruns, Udo Vetter.".
• catalog type "text".