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Transactions of the American Mathematical Society

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Projective modules over subrings of $k[X, Y]$


Author: David F. Anderson
Journal: Trans. Amer. Math. Soc. 240 (1978), 317-328
MSC: Primary 13C10; Secondary 13F20, 14F05
DOI: https://doi.org/10.1090/S0002-9947-1978-0485827-5
MathSciNet review: 0485827
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Abstract: In this paper we study projective modules over subrings of $k[X,Y]$. Conditions are given for projective modules to decompose into free $\oplus$ rank 1 modules. Our main result is that if k is an algebraically closed field and A a subring of $B = k[X,Y]$ with $A \subset B$ integral and ${\text {sing}}(A)$ finite, then all f.g. projective A-modules have the form free $\oplus$ rank 1. We also give several examples of subrings of $k[X,Y]$ which have indecomposable projective modules of rank 2.


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