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

Idempotent factorization of matrices over a Prüfer domain of rational functions

Cossu L.
2022-01-01

Abstract

We consider the smallest subring D of R(X) containing every element of the form 1/(1 + x(2)), with x is an element of R(X). D is a Pruifer domain called the minimal Dress ring of R(X). In this paper, addressing a general open problem for Pruifer non Bezout domains, we investigate whether 2 x 2 singular matrices over D can be decomposed as products of idempotent matrices. We show some conditions that guarantee the idempotent factorization in M-2(D).
2022
Factorization of matrices; idempotent matrices; minimal Dress rings; Pruifer domains
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/404666
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