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Representations under ring extensions: Latimer-MacDuffee and Taussky correspondences. (English) Zbl 0563.13016

The Latimer-MacDuffee duality between similarity classes of nonsingular rational integral \(n\times n\) matrices having a common separable characteristic polynomial f(x) and the classes of faithful ideals in the ring \({\mathbb{Z}}[x]/f(x){\mathbb{Z}}[x]\), is given in this paper from a more general point of view. The semisimple assumption present in previous studies is replaced by the weaker condition that the modules considered become trivial under a suitable extension of the base ring.
Reviewer: Jan Van Geel

MSC:

13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13B02 Extension theory of commutative rings
15B36 Matrices of integers
13A15 Ideals and multiplicative ideal theory in commutative rings
16Gxx Representation theory of associative rings and algebras
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