ON RELATIVE AND BI-RELATIVE ALGEBRAIC K-THEORY OF RINGS OF FINITE CHARACTERISTIC

摘要

Throughout, we fix a prime number p and consider unital associative rings in which p is nilpotent. It was proved by Weibel [28, Cor. 5.3, Cor. 5.4] long ago that for such rings, the relative K-groups associated with a nilpotent extension and the bi-relative K-groups associated with a Milnor square are p-primary torsion groups. However, the question of whether these groups can contain a p-divisible torsion subgroup has remained an open and intractable problem. In this paper, we answer this question in the negative. In effect, we prove the stronger statement that the groups in question are always p-primary torsion groups of bounded exponent.