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- W4366998611 abstract "Let <math xmlns=http://www.w3.org/1998/Math/MathML id=M2> <mi>R</mi> </math> be a ring and let <math xmlns=http://www.w3.org/1998/Math/MathML id=M3> <mi>S</mi> </math> be a multiplicative subset of <math xmlns=http://www.w3.org/1998/Math/MathML id=M4> <mi>R</mi> </math> . An <math xmlns=http://www.w3.org/1998/Math/MathML id=M5> <mi>R</mi> </math> -module <math xmlns=http://www.w3.org/1998/Math/MathML id=M6> <mi>M</mi> </math> is said to be a <math xmlns=http://www.w3.org/1998/Math/MathML id=M7> <mi>u</mi> </math> - <math xmlns=http://www.w3.org/1998/Math/MathML id=M8> <mi>S</mi> </math> -absolutely pure module if <math xmlns=http://www.w3.org/1998/Math/MathML id=M9> <msubsup> <mrow> <mtext>Ext</mtext> </mrow> <mrow> <mi>R</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msubsup> <mfenced open=( close=) separators=|> <mrow> <mi>N</mi> <mo>,</mo> <mi>M</mi> </mrow> </mfenced> </math> is <math xmlns=http://www.w3.org/1998/Math/MathML id=M10> <mi>u</mi> </math> - <math xmlns=http://www.w3.org/1998/Math/MathML id=M11> <mi>S</mi> </math> -torsion for any finitely presented <math xmlns=http://www.w3.org/1998/Math/MathML id=M12> <mi>R</mi> </math> -module <math xmlns=http://www.w3.org/1998/Math/MathML id=M13> <mi>N</mi> </math> . This paper introduces and studies the notion of <math xmlns=http://www.w3.org/1998/Math/MathML id=M14> <mi>S</mi> </math> -FP-projective modules, which extends the classical notion of FP-projective modules. An <math xmlns=http://www.w3.org/1998/Math/MathML id=M15> <mi>R</mi> </math> -module <math xmlns=http://www.w3.org/1998/Math/MathML id=M16> <mi>M</mi> </math> is called an <math xmlns=http://www.w3.org/1998/Math/MathML id=M17> <mi>S</mi> </math> -FP-projective module if <math xmlns=http://www.w3.org/1998/Math/MathML id=M18> <msubsup> <mrow> <mtext>Ext</mtext> </mrow> <mrow> <mi>R</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msubsup> <mfenced open=( close=) separators=|> <mrow> <mi>M</mi> <mo>,</mo> <mi>N</mi> </mrow> </mfenced> <mo>=</mo> <mn>0</mn> </math> for any <math xmlns=http://www.w3.org/1998/Math/MathML id=M19> <mi>u</mi> </math> - <math xmlns=http://www.w3.org/1998/Math/MathML id=M20> <mi>S</mi> </math> -absolutely pure <math xmlns=http://www.w3.org/1998/Math/MathML id=M21> <mi>R</mi> </math> -module <math xmlns=http://www.w3.org/1998/Math/MathML id=M22> <mi>N</mi> </math> . We also introduce the <math xmlns=http://www.w3.org/1998/Math/MathML id=M23> <mi>S</mi> </math> -FP-projective dimension of a module and the global <math xmlns=http://www.w3.org/1998/Math/MathML id=M24> <mi>S</mi> </math> -FP-projective dimension of a ring. Then, the relationship between the <math xmlns=http://www.w3.org/1998/Math/MathML id=M25> <mi>S</mi> </math> -FP-projective dimension and other homological dimensions is discussed." @default.
- W4366998611 created "2023-04-27" @default.
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- W4366998611 date "2023-04-25" @default.
- W4366998611 modified "2023-10-15" @default.
- W4366998611 title "<math xmlns=http://www.w3.org/1998/Math/MathML id=M1> <mi>S</mi> </math>-FP-Projective Modules and Dimensions" @default.
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- W4366998611 doi "https://doi.org/10.1155/2023/7151101" @default.
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