Abstract:
The stable rank of a ring, introduced by Bass and Vaserstein, is an important invariant in algebraic K-theory, but, we think, underappreciated in commutative ring theory. The stable rank of a ring R is comparable to its Krull dimension: for Prüfer rings at least, it is always bounded from above by dim(R)+1, but it is not really a
measure of dimension, since it equals 1 for every local ring. We will show that stable rank equals 2 for some 2-dimensional Prüfer rings, namely, rings of integer-valued polynomials over rings of integers in number fields, and discuss possible generalizations.
Stable rank in commutative ring theory
13.03.2024 14:45 - 16:30
Organiser:
B. Szendroi, R.I. Bot
Location:
Skylounge