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• W2951968129 abstract "Given positive integers e and s we consider Gorenstein Artinian local rings R of embedding dimension e whose maximal ideal $mathfrak{m}$ satisfies $mathfrak{m}^sne 0=mathfrak{m}^{s+1}$. We say that R is a compressed Gorenstein local ring when it has maximal length among such rings. It is known that generic Gorenstein Artinian algebras are compressed. If $sne 3$, we prove that the Poincare series of all finitely generated modules over a compressed Gorenstein local ring are rational, sharing a common denominator. A formula for the denominator is given. When s is even this formula depends only on the integers e and s. Note that for $s=3$ examples of compressed Gorenstein local rings with transcendental Poincare series exist, due to B{o}gvad." @default.
• W2951968129 created "2019-06-27" @default.
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• W2951968129 date "2012-11-28" @default.
• W2951968129 modified "2023-09-27" @default.
• W2951968129 title "Poincar'e series of modules over compressed Gorenstein local rings" @default.
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