On the Dimension Theory of Polynomial Rings over Pullbacks

Details On the Dimension Theory of Polynomial Rings over Pullbacks On the Dimension Theory of Polynomial Rings over Pullbacks

2006-06-27

arxiv.org/abs/math/0606686v1

Mathematics

Commutative Algebra

13 pages, 2 figures, to appear in "Multiplicative Ideal Theory: a tribute to the work of Robert Gilmer," Eds: J. W. Brewer, S.

Scientific paper

This review paper deals with dimension theory of polynomial rings over certain families of pullbacks. While the literature is plentiful, this field is still developing and many contexts are yet to be explored. I will thus restrict the scope of the present survey, mainly, to topics I have worked on over the last decade. The set of pullback constructions studied includes D+M, D+(X_{1}, >..., X_{n})D_{S}[X_{1}, ..., X_{n}], A+XB[X], and D+I.

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