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2017 Direct summands of infinite-dimensional polynomial rings
Mohsen Asgharzadeh, Mehdi Dorreh, Massoud Tousi
J. Commut. Algebra 9(1): 1-19 (2017). DOI: 10.1216/JCA-2017-9-1-1

Abstract

Let $k$ be a field and $R$ a pure subring of the infinite-dimensional polynomial ring $k[X_1,\ldots ]$. If $R$ is generated by monomials, then we show that the equality of height and grade holds for all ideals of~$R$. Also, we show $R$ satisfies the weak Bourbaki unmixed property. As an application, we give the Cohen-Macaulay property of the invariant ring of the action of a linearly reductive group acting by $k$-automorphism on $k[X_1,\ldots ]$. This provides several examples of non Noetherian Cohen-Macaulay rings (e.g., Veronese, determinantal and Grassmanian rings).

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Mohsen Asgharzadeh. Mehdi Dorreh. Massoud Tousi. "Direct summands of infinite-dimensional polynomial rings." J. Commut. Algebra 9 (1) 1 - 19, 2017. https://doi.org/10.1216/JCA-2017-9-1-1

Information

Published: 2017
First available in Project Euclid: 5 April 2017

zbMATH: 06702370
MathSciNet: MR3631823
Digital Object Identifier: 10.1216/JCA-2017-9-1-1

Subjects:
Primary: 13A50 , 13C14

Keywords: Cohen-Macaulay ring , direct summand , non-Noetherian ring , polynomial ring , purity

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.9 • No. 1 • 2017
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