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Catalogue Information
Field name	Details
Dewey Class	512.2
Title	Determinantal Rings ([EBook] /) / by Winfried Bruns, Udo Vetter.
Author	Bruns, Winfried
Added Personal Name	Vetter, Udo author.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1988.
Physical Details	VIII, 240 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1327
ISBN	9783540392743
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0080378
Links to Related Works	Subject References: Group theory . Group Theory and Generalizations . Lie groups . Mathematics . Topological groups . Topological groups, Lie groups . Authors: Bruns, Winfried . Vetter, Udo . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 512.2 .

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Determinantal Rings

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