SP-Domains are Almost Dedekind — A Streamlined Proof
Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 1, pp. 21-24
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Let D be a domain. By [4], D has “property SP” if every ideal of D is a product of radical ideals. It is natural to consider property SP after studying Dedekind domains, which involve factoring ideals into prime ideals. In their article [4] Vaughan and Yeagy prove that a domain having property SP is an almost Dedekind domain. We give a very short and easy proof of this result.
Keywords:
SP-domain, almost Dedekind domain, discrete valuation domain
@article{DMGAA_2020_40_1_a1,
author = {Ahmed, Malik Tusif},
title = {SP-Domains are {Almost} {Dedekind} {\textemdash} {A} {Streamlined} {Proof}},
journal = {Discussiones Mathematicae. General Algebra and Applications},
pages = {21--24},
publisher = {mathdoc},
volume = {40},
number = {1},
year = {2020},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGAA_2020_40_1_a1/}
}
TY - JOUR AU - Ahmed, Malik Tusif TI - SP-Domains are Almost Dedekind — A Streamlined Proof JO - Discussiones Mathematicae. General Algebra and Applications PY - 2020 SP - 21 EP - 24 VL - 40 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMGAA_2020_40_1_a1/ LA - en ID - DMGAA_2020_40_1_a1 ER -
Ahmed, Malik Tusif. SP-Domains are Almost Dedekind — A Streamlined Proof. Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 1, pp. 21-24. http://geodesic.mathdoc.fr/item/DMGAA_2020_40_1_a1/