Geodesic
Projective Ideals of Finite Type
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1057-1061

Voir la notice de l'article provenant de la source Cambridge University Press

The main results in this paper relate the concepts of flatness and projectiveness for finitely generated ideals in a commutative ring with unity. In this discussion the idea of a multiplicative ideal is used. Definition.An ideal Jis multiplicative if and only if whenever I is an ideal with I ⊂ J there exists an ideal Csuch that I = JC.Throughout this paper Rwill denote a commutative ring with unity. If I and Jare ideals of R,then I: J = {x| xJ ⊂ I}. By “prime ideal” we will mean “proper prime ideal” and Specie will denote this set of ideals. Ris called a local ring if it has a unique maximal ideal (the ring need not be Noetherian). If P is in Spec R then RP is the quotient ring formed using the complement of P. 
Smith, William W. Projective Ideals of Finite Type. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1057-1061. doi: 10.4153/CJM-1969-116-7
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[1] 1. Bourbaki, N., Eléments de mathématique, Fasc. 27, Algèbre commutative] chapitre 1: Modules plats; chapitre 2: Localisation; Actualités Sci. Indust., No. 1290 (Hermann, Paris, 1961). Google Scholar

[2] 2. Cartan, H. and Eilenberg, S., Homological algebra (Princeton Univ. Press, Princeton, N.J., 1956). Google Scholar

[3] 3. MacRae, R. E., On an application of the Fitting invariants, J. Algebra 2 (1965), 153–169. Google Scholar

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