Abstract
Let R be a Noetherian commutative ring with dim RD d and let l be an ideal of R. For an integer n such that 2n dC 3, we define a relative Euler class group E n .R; lI R/. Using this group, in analogy to homology sequence of the K0-group, we construct an exact sequence E n .R; lI R/ E. p2/ ! E n .RI R/ E./ ! E n .R= lI R= l/; 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 0! E n .RTtU;.t/I RTtU/ E. p2/ ! E n .RTtUI RTtU/ E./ ! E n .RI R/! 0
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