Vorst, Ton Polynomial extensions and excision for \(K_1\). (English) Zbl 0426.13005 Math. Ann. 244, 193-204 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 13 Documents 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 Keywords:K1; K-theory; polynomial extension; excision; Serre problem Citations:Zbl 0415.13005 PDFBibTeX XMLCite \textit{T. Vorst}, Math. Ann. 244, 193--204 (1979; Zbl 0426.13005) Full Text: DOI EuDML 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.