Geodesic
SP-Domains are Almost Dedekind — A Streamlined Proof
Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 1, pp. 21-24 Cet article a éte moissonné depuis la source Library of Science

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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 
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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/

[1] M.T. Ahmed and T. Dumitrescu, SP-rings with zero-divisors, Comm. Algebra 45 (3) (2017) 4435–4443. doi:10.1080/00927872.2016.1267184

[2] R. Gilmer, Multiplicative Ideal Theory, Queen’s papers Pure Appl. Math. 90 (Queen’s University, Kingston, Ontario, 1992).

[3] B. Olberding, Factorization into radical ideals, Arithmetical properties of commutative rings and monoids (S. Chapman, Ed.), Lecture Notes in Pure Appl. Math. 241 (Chapman & Hall, 2005) 363–377. doi:10.1201/9781420028249

[4] N.H. Vaughan, R.W. Yeagy, Factoring ideals into semiprime ideals, Canad. J. Math. XXX (6) (1978) 1313–1318. doi:10.4153/CJM-1978-108-5