A test theorem on coherent GCD domains
A test theorem on coherent GCD domains
Let <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> be a commutative indecomposable coherent ring. Then the following statements are equivalent: (i) <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 a GCD domain; (ii) <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper …