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Homology sequence and
excision theorem for Euler class group
Yong Yang |
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Vol. 249 (2011), No. 1, 237–254
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Abstract |
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Let R be a Noetherian commutative ring with dimR = d and let l be an ideal of R. For an integer n such that 2n ≥ d + 3, we define a relative Euler class group En(R,l;R). Using this group, in analogy to homology sequence of the K0-group, we construct an exact sequence  called the homology sequence of the Euler class group. The excision theorem in K-theory has a corresponding theorem for the Euler class group. An application is that for polynomial and Laurent polynomial rings, we get short split exact sequences ![n E (p2) n E(ρ) n
0 → E (R [t],(t);R [t])−−−−→ E (R[t];R[t])−−−→ E (R;R) → 0](a121x.png) and ![n −1 −1 E (p2) n −1 −1
0 → E (R[t,t ],(t− 1);R[t,t ])−−−−→ E (R[t,t ];R[t,t ])
E(ρ) n
−−−→ E (R;R) → 0.](a122x.png) |
Keywords
Euler class group, K-theory, excision theorem
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Mathematical Subject Classification 2000
Primary: 13C10
Secondary: 13B25
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Milestones
Received: 17 April 2010
Revised: 27 May 2010
Accepted: 14 June 2010
Published: 3 January 2011
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Authors |
| Yong Yang | |
| Department of Mathematics and
Systems Science National University of Defense Technology Changsha, Hunan 410073 China |
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