Idempotent factorization of matrices over a Prüfer domain of rational functions
Abstract
We consider the smallest subring D of R(X) containing every element of the form 1/(1+x2), with x ϵ R(X). D is a Prüfer domain called the minimal Dress ring of R(X). In this paper, addressing a general open problem for Prüfer non Bézout domains, we investigate whether 2x2 singular matrices over D can be decomposed as products of idempotent matrices. We show some conditions that guarantee the idempotent factorization in M2(D).
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