Abstract
In this article we want to supplement the theory of algebras with straightening law, ASLs for short, by two additions. The first addition concerns the arithmetical rank of ideals generated by an ideal of the poset underlying the ASL. (The arithmetical rank is the least number of elements generating an ideal up to radical.) It turns out that there is a general upper bound only depending on the combinatorial data of the poset. In particular we discuss ideals generated by monomials and show that the ideas leading to the general bound can be used to derive sharper results in this special case. On the other hand there exists a class of ASLs, called symmetric, in which the general bound is always precise. This class includes the homogeneous coordinate rings of Grassmannians, and perhaps the most prominent result in this context is the determination of the least number of equations defining a Schubert subvariety of a Grassmannian.
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© 1989 Springer-Verlag New York Inc.
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Bruns, W. (1989). Additions to the Theory of Algebras with Straightening Law. In: Hochster, M., Huneke, C., Sally, J.D. (eds) Commutative Algebra. Mathematical Sciences Research Institute Publications, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3660-3_6
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DOI: https://doi.org/10.1007/978-1-4612-3660-3_6
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