FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3203165423> ?p ?o ?g. }

• W3203165423 endingPage "152" @default.
• W3203165423 startingPage "133" @default.
• W3203165423 abstract "Given a complete local (Noetherian) ring <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper T> <mml:semantics> <mml:mi>T</mml:mi> <mml:annotation encoding=application/x-tex>T</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we find necessary and sufficient conditions on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper T> <mml:semantics> <mml:mi>T</mml:mi> <mml:annotation encoding=application/x-tex>T</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that there exists a local domain <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=StartAbsoluteValue upper A EndAbsoluteValue greater-than StartAbsoluteValue upper T EndAbsoluteValue> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mi>A</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mo>></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mi>T</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>|A| > |T|</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ModifyingAbove upper A With caret equals upper T> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>A</mml:mi> <mml:mo>^<!-- ^ --></mml:mo> </mml:mover> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>T</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>widehat {A} = T</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ModifyingAbove upper A With caret> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>A</mml:mi> <mml:mo>^<!-- ^ --></mml:mo> </mml:mover> </mml:mrow> <mml:annotation encoding=application/x-tex>widehat {A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denotes the completion of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with respect to its maximal ideal. We then find necessary and sufficient conditions on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper T> <mml:semantics> <mml:mi>T</mml:mi> <mml:annotation encoding=application/x-tex>T</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that there exists a domain <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ModifyingAbove upper A With caret equals upper T> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>A</mml:mi> <mml:mo>^<!-- ^ --></mml:mo> </mml:mover> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>T</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>widehat {A} = T</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=StartAbsoluteValue normal upper S normal p normal e normal c left-parenthesis upper A right-parenthesis EndAbsoluteValue greater-than StartAbsoluteValue normal upper S normal p normal e normal c left-parenthesis upper T right-parenthesis EndAbsoluteValue> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>S</mml:mi> <mml:mi mathvariant=normal>p</mml:mi> <mml:mi mathvariant=normal>e</mml:mi> <mml:mi mathvariant=normal>c</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mo>></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>S</mml:mi> <mml:mi mathvariant=normal>p</mml:mi> <mml:mi mathvariant=normal>e</mml:mi> <mml:mi mathvariant=normal>c</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>T</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>|mathrm {Spec}(A)| > |mathrm {Spec}(T)|</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Finally, we use “partial completions” to create local rings <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ModifyingAbove upper A With caret equals upper T> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>A</mml:mi> <mml:mo>^<!-- ^ --></mml:mo> </mml:mover> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>T</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>widehat {A} = T</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper S normal p normal e normal c left-parenthesis upper A right-parenthesis> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>S</mml:mi> <mml:mi mathvariant=normal>p</mml:mi> <mml:mi mathvariant=normal>e</mml:mi> <mml:mi mathvariant=normal>c</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>mathrm {Spec}(A)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has varying cardinality in different varieties." @default.
• W3203165423 created "2021-10-11" @default.
• W3203165423 creator A5007881779 @default.
• W3203165423 creator A5030527089 @default.
• W3203165423 creator A5033088959 @default.
• W3203165423 creator A5042170245 @default.
• W3203165423 creator A5078811050 @default.
• W3203165423 date "2021-01-01" @default.
• W3203165423 modified "2023-09-24" @default.
• W3203165423 title "Cardinalities of prime spectra of precompletions" @default.
• W3203165423 cites W140876048 @default.
• W3203165423 cites W1983542958 @default.
• W3203165423 cites W2000424588 @default.
• W3203165423 cites W2014617515 @default.
• W3203165423 cites W2084813762 @default.
• W3203165423 cites W2963863922 @default.
• W3203165423 cites W3119215897 @default.
• W3203165423 cites W4242882045 @default.
• W3203165423 cites W80006342 @default.
• W3203165423 doi "https://doi.org/10.1090/conm/773/15538" @default.
• W3203165423 hasPublicationYear "2021" @default.
• W3203165423 type Work @default.
• W3203165423 sameAs 3203165423 @default.
• W3203165423 citedByCount "0" @default.
• W3203165423 crossrefType "other" @default.
• W3203165423 hasAuthorship W3203165423A5007881779 @default.
• W3203165423 hasAuthorship W3203165423A5030527089 @default.
• W3203165423 hasAuthorship W3203165423A5033088959 @default.
• W3203165423 hasAuthorship W3203165423A5042170245 @default.
• W3203165423 hasAuthorship W3203165423A5078811050 @default.
• W3203165423 hasBestOaLocation W32031654231 @default.
• W3203165423 hasConcept C11413529 @default.
• W3203165423 hasConcept C154945302 @default.
• W3203165423 hasConcept C18903297 @default.
• W3203165423 hasConcept C2776321320 @default.
• W3203165423 hasConcept C2777299769 @default.
• W3203165423 hasConcept C41008148 @default.
• W3203165423 hasConcept C86803240 @default.
• W3203165423 hasConceptScore W3203165423C11413529 @default.
• W3203165423 hasConceptScore W3203165423C154945302 @default.
• W3203165423 hasConceptScore W3203165423C18903297 @default.
• W3203165423 hasConceptScore W3203165423C2776321320 @default.
• W3203165423 hasConceptScore W3203165423C2777299769 @default.
• W3203165423 hasConceptScore W3203165423C41008148 @default.
• W3203165423 hasConceptScore W3203165423C86803240 @default.
• W3203165423 hasLocation W32031654231 @default.
• W3203165423 hasLocation W32031654232 @default.
• W3203165423 hasOpenAccess W3203165423 @default.
• W3203165423 hasPrimaryLocation W32031654231 @default.
• W3203165423 hasRelatedWork W1529400504 @default.
• W3203165423 hasRelatedWork W1892467659 @default.
• W3203165423 hasRelatedWork W2143954309 @default.
• W3203165423 hasRelatedWork W2333703843 @default.
• W3203165423 hasRelatedWork W2334690443 @default.
• W3203165423 hasRelatedWork W2386767533 @default.
• W3203165423 hasRelatedWork W2394022102 @default.
• W3203165423 hasRelatedWork W2469937864 @default.
• W3203165423 hasRelatedWork W2808586768 @default.
• W3203165423 hasRelatedWork W2998403542 @default.
• W3203165423 isParatext "false" @default.
• W3203165423 isRetracted "false" @default.
• W3203165423 magId "3203165423" @default.
• W3203165423 workType "other" @default.