Global dimension of real-exponent polynomial rings

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2023-09-19 DOI:10.2140/ant.2023.17.1779

Nathan Geist, Ezra Miller

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引用次数: 1

Abstract

The ring $R$ of real-exponent polynomials in $n$ variables over any field has global dimension $n + 1$ and flat dimension $n$ . In particular, the residue field $k = R ∕ 𝔪$ of $R$ modulo its maximal graded ideal $𝔪$ has flat dimension $n$ via a Koszul-like resolution. Projective and flat resolutions of all $R$ -modules are constructed from this resolution of $k$ . The same results hold when $R$ is replaced by the monoid algebra for the positive cone of any subgroup of $ℝ^{n}$ satisfying a mild density condition.

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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

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