Abstract
In this chapter we consider only commutative integral domains A (see Chapter 3). Such a ring A can be embedded in its field of fractions, which is the quotient of \(A \times (A\backslash \left\{ 0 \right\})\) by the equivalence relation \({\text{(a,b)}} {\mathcal{R}}{\rm {(c,d)}} \Leftrightarrow {\rm ad = bc}.\) The embedding is the map \(\begin{array}{l}\\a \mapsto (a,1) \\\end{array}\).
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Serre, D. (2010). Matrices with Entries in a Principal Ideal Domain; Jordan Reduction. In: Matrices. Graduate Texts in Mathematics, vol 216. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7683-3_9
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DOI: https://doi.org/10.1007/978-1-4419-7683-3_9
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