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arXiv · 1501.03126

On Cohen-Macaulayness and depth of ideals in invariant rings

Martin Kohls·Müfit Sezer
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Abstract

We investigate the presence of Cohen-Macaulay ideals in invariant rings and show that an ideal of an invariant ring corresponding to a modular representation of a $p$-group is not Cohen-Macaulay unless the invariant ring itself is. As an intermediate result, we obtain that non-Cohen-Macaulay factorial rings cannot contain Cohen-Macaulay ideals. For modular cyclic groups of prime order, we show that the quotient of the invariant ring modulo the transfer ideal is always Cohen-Macaulay, extending a result of Fleischmann.

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Martin Kohls, Müfit Sezer. 2015-01-13. On Cohen-Macaulayness and depth of ideals in invariant rings. https://doi.org/10.1016/j.jpaa.2015.10.014

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