The epimorphic images of a Dedekind domain
HTML articles powered by AMS MathViewer
- by T. Cheatham and E. Enochs
- Proc. Amer. Math. Soc. 35 (1972), 37-42
- DOI: https://doi.org/10.1090/S0002-9939-1972-0302640-X
- PDF | Request permission
Abstract:
We prove that the epimorphic image of a Dedekind domain A is characterized (up to A-isomorphisms) by its torsion submodule (as an A-module) and the torsion-free quotient by its torsion submodule. Necessary and sufficient conditions are given on a torsion and torsion-free A-module in order that they be the corresponding parts of an epimorphic image of A.References
- N. Bourbaki, Éléments de mathématique. Fasc. XXVII. Algèbre commutative. Chaps. 1, 2, Actualités Sci. Indust., no. 1290, Hermann, Paris, 1961. MR 36 #146.
- G. B. Klatt and L. S. Levy, Pre-self-injective rings, Trans. Amer. Math. Soc. 137 (1969), 407–419. MR 236165, DOI 10.1090/S0002-9947-1969-0236165-1
- Nicolae Popescu and Tiberiu Spircu, Quelques observations sur les épimorphismes plats (à gauche) d’anneaux, J. Algebra 16 (1970), 40–59 (French). MR 265413, DOI 10.1016/0021-8693(70)90039-6
- Pierre Mazet, Générateurs, relations et épimorphismes d’anneaux, C. R. Acad. Sci. Paris Sér. A-B 266 (1968), A309–A311 (French). MR 238833 P. Samuel, Séminaire d’algèbre commutative dirigé par Pierre Samuel: 1967/68. Les épimorphismes d’anneaux, Secrétariat mathématique, Paris, 1968. MR 39 #6867.
- L. Silver, Noncommutative localizations and applications, J. Algebra 7 (1967), 44–76. MR 217114, DOI 10.1016/0021-8693(67)90067-1
- Hans Heiner Storrer, Epimorphismen von kommutativen Ringen, Comment. Math. Helv. 43 (1968), 378–401 (German). MR 242810, DOI 10.1007/BF02564404
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 37-42
- MSC: Primary 13G05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0302640-X
- MathSciNet review: 0302640