|
| << previous | next >> |
Journal description
All volumes of the corresponding journal
All issues of the corresponding volume
All articles of the corresponding issues
Details for article 3 of 5 found articles
| Title: |
K-Theory of Free Rings |
| Author: |
Gersten, S. M. |
| Appeared in: |
Communications in algebra |
| Paging: | Volume 1 (1974) nr. 1 pages 39-64 |
| Year: |
1974 |
| Contents: |
The object of this article is to establish the following result (Corollary 3.9 below): If R is a regular right noetherian ring and R{X} is the free associative algebra on the set X, then Kn(R) = Kn(R{X}), where Kn refers to the Quillen K-theory. The result can be stated in the equivalent form that Hn(G1(R),Z) = Hn(G1(R{X}),Z). From this result it follows that if F is a free ring without unit, then Kn(F) = 0, whence free rings are acyclic models for Quillen K-theory (3.11 below). This result in turn enables us to complete Anderson's work [1] in identifying the Quillen K-theory [11] and the K-theory proposed by Gersten [7] and Swan [18] for all rings. We also establish that the natural transformation Kn(R) → Knk-v(R) between the Quillen theory and the K-theory of Karoubi and Villamayor is an isomorphism if R is a supercoherent (Definition 1.2) and regular (Definition 1.3) ring. From this result we can gain some information about the K-theory of group rings of free products of groups (Theorem 5.1). |
| Publisher: |
Taylor & Francis |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 3 of 5 found articles
| << previous | next >> |