Projective modules over subrings of $k[X, Y]$
Author:
David F. Anderson
Journal:
Trans. Amer. Math. Soc. 240 (1978), 317328
MSC:
Primary 13C10; Secondary 13F20, 14F05
DOI:
https://doi.org/10.1090/S00029947197804858275
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 Amodules 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.

D. F. Anderson, Projective modules over subrings of $k[X,Y]$, Dissertation, Univ. of Chicago, Chicago, Ill., 1976.
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© Copyright 1978
American Mathematical Society