Abstract
The author finds sufficient conditions for a right subcommutative ring R to have the property that any ring between R and its classical complete right quotient ring is the classical right quotient ring of R with respect to some multiplicatively closed system. Bibliography of 13 references.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
O. Zariski and P. Samuels, Commutative Algebra (Russian translation], Moscow,1 (1963).
R. Gilmer, and I. Ohm, Integral domains with quotient over-rings, Math. Ann., 153, 97–103 (1964).
W. M. Gunnea, Unique factorization in algebraic function fields, Illinois Math.,5, 425–438 (1964).
E. D. Davis, Overrings of commutative rings. II. Trans. Amer. Math, Soc.,110, 196–212 (1964).
E. D. Davis, Rings of algebraic numbers and functions, Math. Nachr,29, 1–7 (1965).
L. Claborn, Dedekind domains and rings of quotients. Pacif. Math.,15, 59–64 (1965).
I. L. Mott, Integral domains with quotient overrings, Math. Ann.,166, 229–232 (1966).
R. L. Pendleton, A characterization of Q-domains, Bull. Amer. Math. Soc.,72, 499–500 (1966).
D. Barbilian, Teoria aritmetica a idealelor, Bucharest (1956).
E. H. Feller, Properties of primary noncommutative rings, Trans. Amer. Math. Soc.,89, 79–91 (1958).
T. Bucur, Sur le thèoréme de decomposition de Lascer-Noether dans les anneaux subcommutatifs, Rev. Roumaine Math. pures et appl.,8, 565–568 (1963).
I. D. Reid, On subcommutative rings, Acta. Math. Acad. Sci. Hung.,16, 23–26 (1956).
V. P. Elizarov, Two properties of associative rings, Matem. Zametki,2, No. 3, 225–232 (1967).
Additional information
Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 689–694, December, 1967.
Rights and permissions
About this article
Cite this article
Elizarov, V.P. Subcommutative Q-rings. Mathematical Notes of the Academy of Sciences of the USSR 2, 906–909 (1967). https://doi.org/10.1007/BF01473476
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01473476