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Polynomial extensions and excision for \(K_1\). (English) Zbl 0426.13005


MSC:

13D15 Grothendieck groups, \(K\)-theory and commutative rings
13B02 Extension theory of commutative rings
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
13F20 Polynomial rings and ideals; rings of integer-valued polynomials

Citations:

Zbl 0415.13005
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References:

[1] Bass, H.: AlgebraicK-theory. New York: Benjamin 1968 · Zbl 0174.30302
[2] Bass, H.: Some problems in ?classical? algebraicK-theory. Lecture Notes in Mathematics, Vol. 342. Berlin, Heidelberg, New York: Springer 1973 · Zbl 0384.18008
[3] Berger, R., Kiehl, R., Kunz, E., Nastold, H.: Differentialrechnung in der analytischen Geometrie. Lecture Notes in Mathematics, Vol. 38. Berlin, Heidelberg, New York: Springer 1967 · Zbl 0163.03202
[4] Geller, S., Roberts, L.: Excision andK 1-regularity for curves with normal crossings. J. Pure Appl. Algebra15, 11-22 (1979) · Zbl 0415.13002 · doi:10.1016/0022-4049(79)90037-9
[5] Grothendieck, A.: Eléments de géometrie algébrique. IV. Publ. Inst. des Hautes Études Scientifiques (1964)
[6] Keune, F.: The relativization ofK 2. J. Algebra54, 159-177 (1979) · Zbl 0403.18009 · doi:10.1016/0021-8693(78)90024-8
[7] Krusemeyer, M.: Fundamental groups, algebraicK-theory and a problem of Abhyankar. Invent. Math.19, 15-47 (1973) · Zbl 0247.14005 · doi:10.1007/BF01418849
[8] Milnor, J.: Introduction to algebraicK-theory. Ann. Math. Studies 72. Princeton: Princeton University Press 1971 · Zbl 0237.18005
[9] Pedrini, C.: On the algebraicK-theory of affine curves. Boll. U.M.I.4, 856-873 (1974) · Zbl 0327.14006
[10] Quillen, D.: Projective modules over polynomial rings. Invent. Math.36, 167-171 (1976) · Zbl 0337.13011 · doi:10.1007/BF01390008
[11] Suslin, A.: On the structure of the special linear group over polynomial rings. Izv. Akad. Nauk S.S.S.R. Ser. Mat.41, 235-252 (1977) · Zbl 0354.13009
[12] Swan, R.: Excision in algebraicK-theory. J. Pure Appl. Algebra1, 221-252 (1974) · Zbl 0262.16025 · doi:10.1016/0022-4049(71)90020-X
[13] Swan, R.: Projective modules over Laurent polynomial rings. Trans. Am. Math. Soc.237, 111-120 (1978) · Zbl 0404.13006 · doi:10.1090/S0002-9947-1978-0469906-4
[14] Traverso, C.: Seminormality and Picard group. Ann. Scuola Norm. Sup. Pisa24, 585-595 (1970) · Zbl 0205.50501
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