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Porter, Timothy

Reduced powers, ultrapowers and exactness of limits. (English) Zbl 0506.18006

J. Pure Appl. Algebra 26, 325-330 (1982).
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MSC:

18G10 Resolutions; derived functors (category-theoretic aspects)
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
16D50 Injective modules, self-injective associative rings

Keywords:

ultrapowers; compact modules; derived functors; reduced powers; equational compactness; linear compactness; inverse limit functor; cosimplicial modules

Citations:

Zbl 0238.18007; Zbl 0259.55004; Zbl 0068.244; Zbl 0463.16001
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Full Text: DOI

References:

[1] Bousfield, A. K.; Kan, D. M., Homotopy Limits, Completions and Localizations, (Lecture Notes in Math. No. 304 (1972), Springer: Springer Berlin) · Zbl 0259.55004
[2] Daley, D. K., Equational Compactness in Rings, (Lecture Notes in Math. No. 745 (1979), Springer: Springer Berlin) · Zbl 0463.16001
[3] Edwards, D.; Hastings, H., Čech and Steenrod Homotopy Theories with Applications to Geometric Topology, (Lecture Notes in Math. No. 542 (1976), Springer: Springer Berlin) · Zbl 0334.55001
[4] Garavaglia, S., Homology with equationally compact coefficients, Fund. Math. C, 89-95 (1978) · Zbl 0377.55006
[5] Grossman, J., Homotopy groups of pro-spaces, Illinois J. Math., 20, 622-625 (1976) · Zbl 0329.55011
[6] Jensen, C. U., Les Foncteurs Dérivés de \(lim\) et leurs Applications en Theorie des Modules, (Lecture Notes in Math. No. 254 (1972), Springer: Springer Berlin) · Zbl 0238.18007
[7] Warfield, R. B., Purity and algebraic compactness for modules, Pacific J. Math., 28, 699-719 (1969) · Zbl 0172.04801
[8] Frayne, T.; Morel, A. C.; Scott, D. S., Reduced direct products, Fund. Math., 51, 195-228 (1962) · Zbl 0108.00501
[9] Gerstner, O., Algebraische Kompaktheit bei Faktorgruppen von Gruppen Ganzzahliger Abbildungen, Manuscripta Math., 11, 103-109 (1974) · Zbl 0272.20050
[10] Porter, T., Čech and Steenrod homotopy and the Quigley exact couple in strong shape and proper homotopy theory, J. Pure Appl. Algebra, 24, 303-312 (1982) · Zbl 0485.55009
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