This paper seems to nail my question right on the head! Mucho thanks! At 01:20 PM 11/23/2018, W. Edwin Clark wrote:
See the paper Left Eucclidean Rings by H H Brungs, Pacific J Math 1973 https://projecteuclid.org/download/pdf_1/euclid.pjm/1102947704 In particular on page 31 you will find the Corollary:
COROLLARY. If R is a division ring then R_n is left (and right) Euclidean with Ï(M) = n-rank (M) + 1 if M <> 0 and Ï(0) = 0.
Here R_n is the ring of n by n matrices over R. Theorem 1 is a more general statement.
On Fri, Nov 23, 2018 at 3:48 PM Henry Baker <hbaker1@pipeline.com> wrote: Euclidean algorithm / continued fraction on *square matrices* ??
3 issues: left/right variants; how to stop; how to get "smaller" remainder.
Left/right variants: I accept that non-commutativity will produce 2 variants.
How to stop: det(remainder)=0
What is the definition of "smaller" in:
remainder = dividend - quotient*divisor,
such that norm(remainder)<norm(divisor)
I.e., what should be the definition of norm(), or are there multiple definitions that work?