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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Projective modules over subrings of $k[X, Y]$
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by David F. Anderson PDF
Trans. Amer. Math. Soc. 240 (1978), 317-328 Request permission

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.
References
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • 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