Noetherianity and Ext

E. L. Green; N. Snashall; Solberg; D. Zacharia

doi:10.1016/j.jpaa.2007.10.011

Noetherianity and Ext

E. L. Green, N. Snashall, Solberg, D. Zacharia

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let R = R₀ ⊕ R₁ ⊕ R₂ ⊕ ⋯ be a graded algebra over a field K such that R₀ is a finite product of copies of K and each R_i is finite dimensional over K. Set J = R₁ ⊕ R₂ ⊕ ⋯ and S = ⊕_{n ≥ 0} Ext_Rⁿ (R / J, R / J). We study the properties of the categories of graded R-modules and S-modules that relate to the noetherianity of R. We pay particular attention to the case when R is a Koszul algebra and S is the Koszul dual to R.

Original language	English (US)
Pages (from-to)	1612-1625
Number of pages	14
Journal	Journal of Pure and Applied Algebra
Volume	212
Issue number	7
DOIs	https://doi.org/10.1016/j.jpaa.2007.10.011
State	Published - Jul 2008

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2007.10.011

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title = "Noetherianity and Ext",

abstract = "Let R = R0 ⊕ R1 ⊕ R2 ⊕ ⋯ be a graded algebra over a field K such that R0 is a finite product of copies of K and each Ri is finite dimensional over K. Set J = R1 ⊕ R2 ⊕ ⋯ and S = ⊕n ≥ 0 ExtRn (R / J, R / J). We study the properties of the categories of graded R-modules and S-modules that relate to the noetherianity of R. We pay particular attention to the case when R is a Koszul algebra and S is the Koszul dual to R.",

author = "Green, {E. L.} and N. Snashall and Solberg and D. Zacharia",

note = "Funding Information: We thank the referee for pointing out problems in an earlier version of this paper. The first and the fourth authors are supported by grants from NSA. The second author is supported by an LMS Scheme 4 grant. The third author is supported by the “Storforsk” grant no. 167130 from the Research Council of Norway.",

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T1 - Noetherianity and Ext

AU - Green, E. L.

AU - Snashall, N.

AU - Solberg,

AU - Zacharia, D.

N1 - Funding Information: We thank the referee for pointing out problems in an earlier version of this paper. The first and the fourth authors are supported by grants from NSA. The second author is supported by an LMS Scheme 4 grant. The third author is supported by the “Storforsk” grant no. 167130 from the Research Council of Norway.

PY - 2008/7

Y1 - 2008/7

N2 - Let R = R0 ⊕ R1 ⊕ R2 ⊕ ⋯ be a graded algebra over a field K such that R0 is a finite product of copies of K and each Ri is finite dimensional over K. Set J = R1 ⊕ R2 ⊕ ⋯ and S = ⊕n ≥ 0 ExtRn (R / J, R / J). We study the properties of the categories of graded R-modules and S-modules that relate to the noetherianity of R. We pay particular attention to the case when R is a Koszul algebra and S is the Koszul dual to R.

AB - Let R = R0 ⊕ R1 ⊕ R2 ⊕ ⋯ be a graded algebra over a field K such that R0 is a finite product of copies of K and each Ri is finite dimensional over K. Set J = R1 ⊕ R2 ⊕ ⋯ and S = ⊕n ≥ 0 ExtRn (R / J, R / J). We study the properties of the categories of graded R-modules and S-modules that relate to the noetherianity of R. We pay particular attention to the case when R is a Koszul algebra and S is the Koszul dual to R.

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JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

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Noetherianity and Ext

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