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A note on non-unique factorization domains (UFD)

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Abstract

In the paper ‘On GCD and LCM in Domains — A Conjecture of Gauss’ in Resonance [1], some elegant proofs for the fact that ℤ[\( \sqrt { - d} \)] (d ≥ 3, quare-free) is not a UFD are given. The aim of this note is to provide an alternative proof for this theorem.

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Suggested Reading

  1. D Khurana, On GCD and LCM in Domains — A Conjecture of Gauss, Resonance, Vol.8, No.6, pp.72–79, 2003.

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  2. V Peric, M Vukovic, Some examples of principal domain which is not Euclidean and some other counterexamples, Novi Sad J. Math, Vol.38, No. 1, pp.137–154, 2008.

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  1. Faculty of Mathematics and Computer Science, West University of Timisoara, Bv. V parvan 4, 300223, Timisoara, Romania

    Dorel Mihet

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  1. Dorel Mihet
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Correspondence to Dorel Mihet.

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Mihet, D. A note on non-unique factorization domains (UFD). Reson 15, 737–739 (2010). https://doi.org/10.1007/s12045-010-0083-8

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  • DOI: https://doi.org/10.1007/s12045-010-0083-8

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