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- W3119866105 abstract "A quaternion order <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper O> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>O</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {O}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> over a Dedekind domain <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 Bass if every <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>-superorder is Gorenstein, and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper O> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>O</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {O}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is basic if it contains an integrally closed quadratic <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>-order. In this article, we show that these conditions are equivalent in local and global settings: a quaternion order is Bass if and only if it is basic. In particular, we show that the property of being basic is a local property of a quaternion order." @default.
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- W3119866105 date "2021-01-13" @default.
- W3119866105 modified "2023-10-11" @default.
- W3119866105 title "On basic and Bass quaternion orders" @default.
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- W3119866105 doi "https://doi.org/10.1090/bproc/68" @default.
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