Duality and noncommutative planes
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Duality and noncommutative planes. / Jøndrup, Søren.
In: Journal of Pure and Applied Algebra, Vol. 219, No. 3, 2015, p. 563-568.Research output: Contribution to journal › Journal article › Research › peer-review
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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