Type: Article
Publication Date: 1995-01-01
Citations: 3
DOI: https://doi.org/10.1090/s0002-9939-1995-1277104-5
In this paper we prove the following main result. A (commutative integral) domain <italic>R</italic> is a Dedekind domain if and only if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R left-bracket left-bracket upper X right-bracket right-bracket subset-of upper T left-bracket left-bracket upper X right-bracket right-bracket"> <mml:semantics> <mml:mrow> <mml:mi>R</mml:mi> <mml:mo stretchy="false">[</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">]</mml:mo> <mml:mo stretchy="false">]</mml:mo> <mml:mo>⊂</mml:mo> <mml:mi>T</mml:mi> <mml:mo stretchy="false">[</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">]</mml:mo> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">R[[X]] \subset T[[X]]</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is LCM-stable for each domain <italic>T</italic> containing <italic>R</italic> as a subring.