Abstract
It is proved that a commutative ring A is arithmetical if and only if every finitely generated ideal M of the ring A is a quasi-projective A-module and every endomorphism of this module can be extended to an endomorphism of the module A A . These results are proved with the use of some general results on invariant arithmetical rings.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Abuhlail, M. Jarrar, and S. Kabbaj, “Commutative rings in which every finitely generated ideal is quasi-projective,” J. Pure Appl. Algebra, 215, 2504–2511 (2011).
A. A. Tuganbaev, Semidistributive Modules and Rings, Kluwer Academic, Dordrecht (1998).
A. A. Tuganbaev, “Multiplication modules,” J. Math. Sci., 123, No. 2, 3839–3905 (2004).
R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia (1991).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 19, No. 2, pp. 207–211, 2014.
Rights and permissions
About this article
Cite this article
Tuganbaev, A.A. Arithmetical Rings and Quasi-Projective Ideals. J Math Sci 213, 268–271 (2016). https://doi.org/10.1007/s10958-016-2715-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-016-2715-3