Geodesic
Rings with a free semigroup of invertible ideals
Sbornik. Mathematics, Tome 18 (1972) no. 1, pp. 101-110 
R. B. Treger. Rings with a free semigroup of invertible ideals. Sbornik. Mathematics, Tome 18 (1972) no. 1, pp. 101-110. http://geodesic.mathdoc.fr/item/SM_1972_18_1_a6/
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In this paper commutative rings with a free semigroup of invertible ideals are characterized. It is shown, in particular, that a domain is a ring in which a principal ideal can be decomposed into a product of prime ideals. Bibliography: 8 titles.

[1] J. Lambek, Lectures on rings and modules, Blaisdell Publ. Co., Waltham, 1966 | MR | Zbl

[2] W. W. Smith, “Projective ideals of finite type”, Canad. J. Math., 21:5 (1969), 1057–1061 | MR | Zbl

[3] A. Kartani, S. Eilenberg, Gomologicheskaya algebra, IL, Moskva, 1960

[4] O. Zarisskii, P. Samyuel, Kommutativnaya algebra, t. I, IL, Moskva, 1963

[5] M. Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, no. 13, Intercience Publ., New York–London, 1962 | MR | Zbl

[6] I. Kaplanskii, Proektivnye moduli, Matematika, 4, no. 1, 1960

[7] R. B. Treger, “$O_z^l$-koltsa”, XI Vsesoyuznyi algebraicheskii kollokvium, Rezyume soobschenii i dokladov, Kishinev, 1971

[8] H. Bass, Algebraic $K$-theory, Benjamin, Inc., New York–Amsterdam, 1968 | MR | Zbl