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Algebraic L ‐Theory, II: Laurent Extensions
Author(s) -
Ranicki A. A.
Publication year - 1973
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-27.1.126
Subject(s) - mathematics , algebraic number , pure mathematics , algebra over a field , mathematical analysis
where Az = A[z, z ] is the Laurent extension ring of A, with involution z h> z~. (Cf. Part III, [5], for the generalization to twisted Laurent extensions.) Similar splittings arise in [3]—indeed, our method of proof follows that of [3], except that Novikov neglects 2-torsion in the Z-groups, and assumes that 2 is invertible in A. In the geometrically realizable case A = Z[TT], (TT a finitely presented group), it is possible to obtain the decompositions by topological methods ([2], [6], and [8]). Defining X-theories L^^A) for m < 2, n (mod 4) by