Modules with Artinian prime factors
HTML articles powered by AMS MathViewer
- by Efraim P. Armendariz PDF
- Proc. Amer. Math. Soc. 78 (1980), 311-314 Request permission
Abstract:
An R-module M has Artinian prime factors if $M/PM$ is an Artinian module for each prime ideal P of R. For commutative rings R it is shown that Noetherian modules with Artinian prime factors are Artinian. If R is either commutative or a von Neumann regular V-ring then the endomorphism ring of a module with Artinian prime factors is a strongly $\pi$-regular ring.References
- E. P. Armendariz and Joe W. Fisher, Regular $P.I.$-rings, Proc. Amer. Math. Soc. 39 (1973), 247–251. MR 313305, DOI 10.1090/S0002-9939-1973-0313305-3
- Efraim P. Armendariz, Joe W. Fisher, and Robert L. Snider, On injective and surjective endomorphisms of finitely generated modules, Comm. Algebra 6 (1978), no. 7, 659–672. MR 469974, DOI 10.1080/00927877808822263
- William D. Blair, Right Noetherian rings integral over their centers, J. Algebra 27 (1973), 187–198. MR 325679, DOI 10.1016/0021-8693(73)90173-7
- John Cozzens and Carl Faith, Simple Noetherian rings, Cambridge Tracts in Mathematics, No. 69, Cambridge University Press, Cambridge-New York-Melbourne, 1975. MR 0396660 F. Dischinger, On strongly $\pi$-regular rings, C. R. Acad. Sci. 285 (1976), 571-573.
- Joe W. Fisher, Nil subrings of endomorphism rings of modules, Proc. Amer. Math. Soc. 34 (1972), 75–78. MR 292878, DOI 10.1090/S0002-9939-1972-0292878-2
- K. R. Goodearl, Artinian and Noetherian modules over regular rings, Comm. Algebra 8 (1980), no. 5, 477–504. MR 561542, DOI 10.1080/00927878008822470
- Nathan Jacobson, Structure of rings, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, 190 Hope Street, Providence, R.I., 1956. MR 0081264
- Robert W. Miller and Darrell R. Turnidge, Some examples from infinite matrix rings, Proc. Amer. Math. Soc. 38 (1973), 65–67. MR 310001, DOI 10.1090/S0002-9939-1973-0310001-3
- Morris Orzech, Onto endomorphisms are isomorphisms, Amer. Math. Monthly 78 (1971), 357–362. MR 280475, DOI 10.2307/2316897
- Hans Heiner Storrer, Epimorphismen von kommutativen Ringen, Comment. Math. Helv. 43 (1968), 378–401 (German). MR 242810, DOI 10.1007/BF02564404
- Wolmer V. Vasconcelos, On finitely generated flat modules, Trans. Amer. Math. Soc. 138 (1969), 505–512. MR 238839, DOI 10.1090/S0002-9947-1969-0238839-5
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 311-314
- MSC: Primary 16A30; Secondary 16A46, 16A64
- DOI: https://doi.org/10.1090/S0002-9939-1980-0553364-X
- MathSciNet review: 553364