# Download e-book for iPad: Algebraic K-Theory: Proceedings of the Conference Held at by Michaeol J. Stein

By Michaeol J. Stein

ISBN-10: 3540079963

ISBN-13: 9783540079965

ISBN-10: 3540379649

ISBN-13: 9783540379645

Read Online or Download Algebraic K-Theory: Proceedings of the Conference Held at Northwestern University Evanston, January 12–16, 1976 PDF

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Extra info for Algebraic K-Theory: Proceedings of the Conference Held at Northwestern University Evanston, January 12–16, 1976

Sample text

AS/J is special. 1SKI(AS/J ) ~ S K I ( R X ) ~ { f ~ A I f(x) = O ~ K'o-l(x). Now for each x ~ X, M x = is a maximal ideal of A disjoint from S. ideal of A not contained some Mx, x E X. Thus Suppose I is an Then since X is compact we can find fl' f2 ..... -,4 f c I N S. Thus any ideal of A disjoint from S is contained in some M x so the maximal ideals of A S are the ideals (Mx) S, x ~ X. Since J is 37 the intersection of these ideals, J is the Jacobson radical of AS. It follows from[Bass, Chap.

Of Sl this latter group is Z2. Here SKI(A) Since X has the homotopy type ~ SKI(A) is not surjective. 5. Let B = R[x,y]/(x 2 + y2 - l ) viewed as a subalgebra of the algebra of continuous real valued functions on the arc S) Then SKI(B } = Z 2 but S K I ( B ) ~ S K I ( B ) ~ [ S SKI(B) ----~SKI(w is not injective. = ~(x,y) ~ R2 Ix2 + 2 2 = l,x o). ~, SL(R)] ~ [I, SL(R)] = O. 2. 5: Let A = R[Xl,X 2 ..... Xn], X a connected compact subset of R n and S = ~f ~ A I f does not vanish on X). Proof: on X.

Z~ Xn ] ~ KO(Z~). 41 commutes where K,p are the inclusion and projection. 1 Thus (2) gives the split exact (3) 0 - ~ K1(PK) KI(A) > Kl(z~) ~ Ko(~nA) - Let ~ji = {(Xl . . Xn ) ~ I nlxj = i } j = 1,2 . . n; i = 0,I be a face of Now the algebra of polynomial functions on a~ is isomorphic to A [ t l , , . SAn ~ ~ A[t I , . (u)j is a unit of A[t I , . regular, must be constant. and so, since unit in A. 2: Let A = R. Since ,tn_ I ] \$o Now i f u is a are constant on each face of ~I n must be constant, i .