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K ‐Theoretic Properties of Generic Matrix Rings
Author(s) -
Coutinho S. C.
Publication year - 1985
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-32.1.51
Subject(s) - mathematics , abelian group , rank (graph theory) , ring (chemistry) , matrix (chemical analysis) , combinatorics , zero (linguistics) , field (mathematics) , pure mathematics , group (periodic table) , discrete mathematics , physics , quantum mechanics , chemistry , linguistics , philosophy , organic chemistry , chromatography
Let R 2, n be the ring of n generic 2 × 2 matrices over a field of characteristic zero. We show that K 0 ( R 2, 2 ) ≃ Z, K 0 ( R 2, 3 ) ≄ Z and K 1 ( R 2, 2 )≃ k ⊕ A , where A is a free abelian group of infinite rank.