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arXiv · 1303.3937

Krull dimension and Monomial Orders

Gregor Kemper·Ngo Viet Trung
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Abstract

We introduce the notion of independent sequences with respect to a monomial order by using the least terms of polynomials vanishing at the sequence. Our main result shows that the Krull dimension of a Noetherian ring is equal to the supremum of the length of independent sequences. The proof has led to other notions of independent sequences, which have interesting applications. For example, we can characterize the maximum number of analytically independent elements in an arbitrary ideal of a local ring and that dim B is not greater than dim A if B is a subalgebra of A and A is a (not necessarily finitely generated) subalgebra of a finitely generated algebra over a Noetherian Jacobson ring.

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Gregor Kemper, Ngo Viet Trung. 2013-10-07. Krull dimension and Monomial Orders. https://arxiv.org/abs/1303.3937

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