Decomposition theories for abelian categories
HTML articles powered by AMS MathViewer
- by Joe W. Fisher and Harvey Wolff PDF
- Trans. Amer. Math. Soc. 182 (1973), 61-69 Request permission
Abstract:
Both the classical approach to decomposition theories and Fisher’s technique of constructing decomposition theories from radical functions are extended to and exploited in the context of abelian categories. These two different approaches to decomposition theories for abelian categories intertwine in one theorem from which flows necessary and sufficient conditions for the existence of the tertiary, primary, and Bourbaki’s $\mathcal {P}$-primary decomposition theories.References
- N. Bourbaki, Éléments de mathématique. Fasc. X. Première partie. Livre III: Topologie générale. Chapitre 10: Espaces fonctionnels, Hermann, Paris, 1961 (French). Deuxième édition, entièrement refondue; Actualités Sci. Indust., No. 1084. MR 0149429
- Ion Bucur and Aristide Deleanu, Introduction to the theory of categories and functors, Pure and Applied Mathematics, Vol. XIX, John Wiley & Sons, Ltd., London-New York-Sydney, 1968. With the collaboration of Peter J. Hilton and Nicolae Popescu; A Wiley Interscience Publication. MR 0236236
- Joe W. Fisher, Decomposition theories for modules, Trans. Amer. Math. Soc. 145 (1969), 241–269. MR 252436, DOI 10.1090/S0002-9947-1969-0252436-7
- Joe W. Fisher, The primary decomposition theory for modules, Pacific J. Math. 35 (1970), 359–367. MR 274501, DOI 10.2140/pjm.1970.35.359
- John W. Gray, Sheaves with values in a category, Topology 3 (1965), 1–18. MR 159328, DOI 10.1016/0040-9383(65)90066-2
- Alexander Grothendieck, Sur quelques points d’algèbre homologique, Tohoku Math. J. (2) 9 (1957), 119–221 (French). MR 102537, DOI 10.2748/tmj/1178244839
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 182 (1973), 61-69
- MSC: Primary 18E99
- DOI: https://doi.org/10.1090/S0002-9947-1973-0327870-8
- MathSciNet review: 0327870