Duality and noncommutative planes

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Duality and noncommutative planes. / Jøndrup, Søren.

I: Journal of Pure and Applied Algebra, Bind 219, Nr. 3, 2015, s. 563-568.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Jøndrup, S 2015, 'Duality and noncommutative planes', Journal of Pure and Applied Algebra, bind 219, nr. 3, s. 563-568. https://doi.org/10.1016/j.jpaa.2014.05.014

APA

Jøndrup, S. (2015). Duality and noncommutative planes. Journal of Pure and Applied Algebra, 219(3), 563-568. https://doi.org/10.1016/j.jpaa.2014.05.014

Vancouver

Jøndrup S. Duality and noncommutative planes. Journal of Pure and Applied Algebra. 2015;219(3):563-568. https://doi.org/10.1016/j.jpaa.2014.05.014

Author

Jøndrup, Søren. / Duality and noncommutative planes. I: Journal of Pure and Applied Algebra. 2015 ; Bind 219, Nr. 3. s. 563-568.

Bibtex

@article{4a732c453c8b42558993576e5654b968,
title = "Duality and noncommutative planes",
abstract = "We study extensions of simple modules over an associative ring A   and we prove that for twosided ideals mm and nn with artinian factors the condition ExtA1(A/m,A/n)≠0 holds for the left A  -modules A/mA/m and A/nA/n if and only if it holds for the right modules A/nA/n and A/mA/m.The methods proving this are applied to show that noncommutative models of the plane, i.e. algebras of the form k〈x,y〉/(f)k〈x,y〉/(f), where f∈([x,y])f∈([x,y]) are noetherian only in case (f)=([x,y])",
author = "S{\o}ren J{\o}ndrup",
year = "2015",
doi = "10.1016/j.jpaa.2014.05.014",
language = "English",
volume = "219",
pages = "563--568",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier BV * North-Holland",
number = "3",

}

RIS

TY - JOUR

T1 - Duality and noncommutative planes

AU - Jøndrup, Søren

PY - 2015

Y1 - 2015

N2 - We study extensions of simple modules over an associative ring A   and we prove that for twosided ideals mm and nn with artinian factors the condition ExtA1(A/m,A/n)≠0 holds for the left A  -modules A/mA/m and A/nA/n if and only if it holds for the right modules A/nA/n and A/mA/m.The methods proving this are applied to show that noncommutative models of the plane, i.e. algebras of the form k〈x,y〉/(f)k〈x,y〉/(f), where f∈([x,y])f∈([x,y]) are noetherian only in case (f)=([x,y])

AB - We study extensions of simple modules over an associative ring A   and we prove that for twosided ideals mm and nn with artinian factors the condition ExtA1(A/m,A/n)≠0 holds for the left A  -modules A/mA/m and A/nA/n if and only if it holds for the right modules A/nA/n and A/mA/m.The methods proving this are applied to show that noncommutative models of the plane, i.e. algebras of the form k〈x,y〉/(f)k〈x,y〉/(f), where f∈([x,y])f∈([x,y]) are noetherian only in case (f)=([x,y])

U2 - 10.1016/j.jpaa.2014.05.014

DO - 10.1016/j.jpaa.2014.05.014

M3 - Journal article

VL - 219

SP - 563

EP - 568

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 3

ER -

ID: 95291467