Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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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 (Department of Mathematics Education, and Institute of Pure and Applied Mathematics Chonbuk National University) ;
  • Kim, Sang-hee (Department of Mathematics Chosun University)
  • Received : 2017.11.15
  • Accepted : 2017.12.15
  • Published : 2017.12.25
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Abstract

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 $Ker({\varphi})=SL_R(P)$.

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References

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