Duality and noncommutative planes

TY - JOUR

T1 - Duality and noncommutative planes

AU - Jøndrup, Søren

PY - 2015/3/1

Y1 - 2015/3/1

N2 - We study extensions of simple modules over an associative ring A and we prove that for twosided ideals m and n with artinian factors the condition ExtA1(A/m,A/n)≠0 holds for the left A-modules A/m and A/n if and only if it holds for the right modules A/n and A/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), where 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 m and n with artinian factors the condition ExtA1(A/m,A/n)≠0 holds for the left A-modules A/m and A/n if and only if it holds for the right modules A/n and A/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), where 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

SN - 0022-4049

VL - 219

SP - 563

EP - 568

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 3

ER -