ENGLISH

Determinantal Rings

By Winfried Bruns , Udo Vetter (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1988
ISBN
9783540194682, 3540194681
DOI
10.1007/BFb0080378
Language
english
Format
DJVU
Filesize
2 MB (2110803 bytes)
Series
Lecture Notes in Mathematics 1327
Edition
1
Pages
240\244
Topic
Mathematics Algebra
Time added
2010-04-25 21:59:20
Group Theory and Generalizations; Topological GrouLie Groups

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.

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