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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