Open Access
2017 Euler class group of certain overrings of a polynomial ring
Alpesh M. Dhorajia
J. Commut. Algebra 9(3): 341-365 (2017). DOI: 10.1216/JCA-2017-9-3-341


Let $A$ be a commutative Noetherian ring of dimension~$n$ and $P$ a projective $A$-module of rank~$n$ with trivial determinant. In \cite {BR1}, Bhatwadekar and Sridharan defined the $n$th Euler class group of~$A$ and studied the obstruction to the existence of unimodular element in~$P$. For $R=A[T]$ and $R=A[T,T^{-1}]$, the $n$th Euler class groups of $R$ are defined by Das and Keshari in \cite {mkd1, MK1}, under certain assumption on $A$ in the latter case. We define the $n$th Euler class group of the ring $R=A[T,1/f(T)]$, where $f(T)\in A[T]$ is a monic polynomial and the height of the Jacobson radical of $A$ is $\geq 2$. Also, we prove results similar to those in \cite {MK1}.


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Alpesh M. Dhorajia. "Euler class group of certain overrings of a polynomial ring." J. Commut. Algebra 9 (3) 341 - 365, 2017.


Published: 2017
First available in Project Euclid: 1 August 2017

zbMATH: 06790174
MathSciNet: MR3685047
Digital Object Identifier: 10.1216/JCA-2017-9-3-341

Primary: 13C10
Secondary: 13B25

Keywords: projective module , Ring theory , unimodular element

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

Vol.9 • No. 3 • 2017
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