• Title/Summary/Keyword: Projective module with finite rank

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THE DETERMINANT MAP FROM THE AUTOMORPHISM GROUP OF A PROJECTIVE R-MODULE TO THE UNIT GROUP OF R

  • Lee, Sang Cheol;Kim, Sang-hee
    • Honam Mathematical Journal
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    • v.39 no.4
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    • pp.677-688
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    • 2017

  • Let P be a finitely generated projective module over a commutative ring R with identity. If P has finite rank, then it will be shown that the map ${\varphi}:Aut_R(P){\rightarrow}U(R)$ defined by ${\varphi}({\alpha})={\det}({\alpha})$ is locally surjective and $Ker({\varphi})=SL_R(P)$.

  • https://doi.org/10.5831/HMJ.2017.39.4.677 인용 PDF KSCI