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- W1594105856 abstract "Let $K$ be a field and let $mathbb N = {1,2, dots }$. Let $R_n=K[x_{ij} mid 1le ile n, jin mathbb N]$ be the ring of polynomials in $x_{ij}$ $(1 le i le n, j in mathbb N)$ over $K$. Let $S_n = Sym ({1,2, ldots, n })$ and $Sym (mathbb N)$ be the groups of the permutations of the sets ${1,2,dots, n }$ and $mathbb N$, respectively. Then $S_n$ and $Sym (mathbb N)$ act on $R_n$ in a natural way: $tau (x_{ij})=x_{tau(i)j}$ and $sigma (x_{ij})=x_{isigma (j)}$ for all $tau in S_n$ and $sigma in Sym(mathbb N)$. Let $overline{R}_n$ be the subalgebra of the symmetric polynomials in $R_n$, [ overline{R}_n = {f in R_n mid tau (f) = f mbox{for each} tau in S_n } . ] In 1992 the second author proved that if $char (K)= 0$ or $char(K)=p > n$ then every $Sym (mathbb N)$-invariant ideal in $overline{R}_n$ is finitely generated (as such). In this note we prove that this is not the case if $char (K)=ple n$. We also survey some results about $Sym (mathbb N)$-invariant ideals in polynomial algebras and some related results." @default.
- W1594105856 created "2016-06-24" @default.
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- W1594105856 date "2015-03-26" @default.
- W1594105856 modified "2023-10-06" @default.
- W1594105856 title "Symmetric Polynomials and Nonfinitely Generated Sym(ℕ)-Invariant Ideals" @default.
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- W1594105856 doi "https://doi.org/10.1007/s10958-015-2329-1" @default.
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