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Search: MSC category 13F20 ( Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25] )

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1. CMB 1999 (vol 42 pp. 231)

Rush, David E.
Generating Ideals in Rings of Integer-Valued Polynomials
Let $R$ be a one-dimensional locally analytically irreducible Noetherian domain with finite residue fields. In this note it is shown that if $I$ is a finitely generated ideal of the ring $\Int(R)$ of integer-valued polynomials such that for each $x \in R$ the ideal $I(x) =\{f(x) \mid f \in I\}$ is strongly $n$-generated, $n \geq 2$, then $I$ is $n$-generated, and some variations of this result.

Categories:13B25, 13F20, 13F05

2. CMB 1997 (vol 40 pp. 54)

Kechagias, Nondas E.
A note on $U_n\times U_m$ modular invariants
We consider the rings of invariants $R^G$, where $R$ is the symmetric algebra of a tensor product between two vector spaces over the field $F_p$ and $G=U_n\times U_m$. A polynomial algebra is constructed and these invariants provide Chern classes for the modular cohomology of $U_{n+m}$.

Keywords:Invariant theory, cohomology of the unipotent group

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