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- W1552755947 abstract "A <italic>homological degree</italic> of a graded module <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper M> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding=application/x-tex>M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is an extension of the usual notion of multiplicity tailored to provide a numerical signature for the module even when <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper M> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding=application/x-tex>M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is not Cohen–Macaulay. We construct a degree, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=h d e g left-parenthesis upper M right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>hdeg</mml:mi> <mml:mo><!-- --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi>M</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>operatorname {hdeg}(M)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, that behaves well under hyperplane sections and the modding out of elements of finite support. When carried out in a local algebra this degree gives a simulacrum of complexity <italic>à la</italic> Castelnuovo–Mumford’s regularity. Several applications for estimating reduction numbers of ideals and predictions on the outcome of Noether normalizations are given." @default.
- W1552755947 created "2016-06-24" @default.
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- W1552755947 date "1998-01-01" @default.
- W1552755947 modified "2023-09-25" @default.
- W1552755947 title "The homological degree of a module" @default.
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- W1552755947 doi "https://doi.org/10.1090/s0002-9947-98-02127-8" @default.
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