Abstract
A module is said to be distributive if the lattice of all its submodules is distributive. A module is called semidistributive if it is a direct sum of distributive modules. Right semidistributive rings, as well as distributively decomposable rings, are investigated.
Similar content being viewed by others
References
A. A. Tuganbaev, “Direct sums of distributive modules,”Mat. Sb. [Russian Acad. Sci. Sb. Math.],187, No. 12, 137–156 (1996).
M. H. Wright, “Right locally distributive rings,” in:Ring Theory. Proc. Bien. Ohio State, Denison Conf. (Granville, Ohio, May 1992), World Sci. Publ., Singapore (1993), pp. 350–357.
R. Gordon and J. C. Robson, “Krull dimension,”Mem. Amer. Math. Soc.,133, 1–78 (1973).
A. A. Tuganbaev, “Rings whose lattice of right ideals is distributive,”Izv. Vyssh. Uchebn. Zaved. Mat. [Soviet Math. (Iz. VUZ)], No. 2, 44–49 (1986).
T. H. Lenagan, “Noetherian rings with Krull dimension one,”J. London Math. Soc. (2),15, No. 1, 41–47 (1977).
A. A. Tuganbaev, “Distributive semiprime rings,”Mat. Zametki [Math. Notes],58, No. 5, 736–761 (1995).
K. R. Goodearl,Ring Theory. Nonsingular Rings and Modules, Marcel Dekker, New York (1976).
C. Faith,Algebra, Vol. 2, Springeer, Berlin (1976).
C. Faith,Rings, Modules, and Categories, Vol. 1, Springer, Berlin (1973).
W. Stephenson, “Modules whose lattice of submodules is distributive,”Proc. London Math. Soc. (3),28, No. 2, 291–310 (1974).
Author information
Authors and Affiliations
Additional information
Translated fromMatematicheskie Zemetki, Vol. 65, No. 2, pp. 307–313, February, 1999.
Rights and permissions
About this article
Cite this article
Tuganbaev, A.A. Semidistributive and distributively decomposable rings. Math Notes 65, 253–258 (1999). https://doi.org/10.1007/BF02679824
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02679824