Polynomial rings over Goldie rings are often Goldie

Abstract

Here, we prove a result that has as a consequence the fact that if the ring <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is an algebra over an uncountable field the a.c.c. on annihilators is preserved under polynomial extensions by any number of variables.

Locations

• Proceedings of the American Mathematical Society - View - PDF