This article is cited in 2 scientific papers (total in 2 papers)
Ideals in commutative rings
Yu. A. Drozd
This paper deals with one-dimensional (commutative) rings without nilpotent elements such that every ideal is generated by three elements. It is shown that in such rings the square of every ideal is invertible, i.e. divides its multiplier ring. In addition, every ideal is distinguished, in the sense that on localization at any maximal ideal it becomes either principal or dual to a principal ideal. Conversely, if a one-dimensional ring without nilpotent elements satisfies either of these conditions, and if all its residue class fields are $2$-perfect and contain at least three elements, then every ideal can be generated by three elements.
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Mathematics of the USSR-Sbornik, 1976, 30:3, 297–310
MSC: Primary 13A15; Secondary 14A05, 14H20
Yu. A. Drozd, “Ideals in commutative rings”, Mat. Sb. (N.S.), 101(143):3(11) (1976), 334–348; Math. USSR-Sb., 30:3 (1976), 297–310
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\paper Ideals in commutative rings
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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Drozd Yu.A., Skuratovskii R.V., “Cubic Rings and their Ideals”, Ukr. Math. J., 62:4 (2010), 530–536
Yuriy A. Drozd, Ruslan V. Skuratovskii, “One branch curve singularities with at most 2-parameter families of ideals”, Algebra Discrete Math., 13:2 (2012), 209–219
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