Abstract
Let αε{lunate}GLn A be a matrix over a commutative ring A with 1 such that (det α)2 = 1. If α is cyclic, it can be written as a product of at most three involutions. When A satisfies the first Bass stable range condition, then α can be written as a product of at most five involutions. If in addition either n ≤ 3 or n = 4 and det α = -1, then α can be written as a product of at most four involutions. When A is a Dedekind ring of arithmetic type, the number of involutions needed to express α is uniformly bounded for any n ≥ 3. When A = C[x] the number of involutions is unbounded for any n ≥ 2.
Original language | English (US) |
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Pages (from-to) | 37-47 |
Number of pages | 11 |
Journal | Linear Algebra and Its Applications |
Volume | 229 |
Issue number | C |
DOIs | |
State | Published - Nov 1 1995 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics