Abstract
If a ≠ 0 is an element of D them by hypothesis a and a 2 must be associated elements of D. Then a 2 = au for a suitable unit u ∈ D. Hence a(a - u) =0 and a - u = 0, D having no zero divisors. So, each nonzero element in D is a unit.
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© 1998 Springer Science+Business Media Dordrecht
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Cǎlugǎreanu, G., Hamburg, P. (1998). Divisibility in Integral Domains. In: Exercises in Basic Ring Theory. Kluwer Texts in the Mathematical Sciences, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9004-4_23
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DOI: https://doi.org/10.1007/978-94-015-9004-4_23
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4985-8
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