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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Dimension theory


Author: Abraham Zaks
Journal: Proc. Amer. Math. Soc. 38 (1973), 457-464
MSC: Primary 18G20
DOI: https://doi.org/10.1090/S0002-9939-1973-0338130-9
MathSciNet review: 0338130
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Abstract: The $ T$-equivalence and $ T$-iterations introduced for a bifunctor $ T$ enable one to deduce a ``shifting property'' from which one gets the ``long exact sequence of homology.'' Also, the appropriate lemma of Schanuel is proved, from which one can develop a $ T$-dimension theory. These notions are useful in proving known duality homomorphisms and may serve to get some new ones. For one purpose, they unify the methods of studying the various common dimensions.


References [Enhancements On Off] (What's this?)

  • [1] M. Auslander and M. Bridger, Stable module theory, Mem. Amer. Math. Soc. No. 94 (1969). MR 42 #4580. MR 0269685 (42:4580)
  • [2] I. Kaplansky, Commutative rings, Allyn and Bacon, Boston, Mass., 1970. MR 40 #7234. MR 0254021 (40:7234)
  • [3] J. Lambek, Lectures on rings and modules, Blaisdell, Waltham, Mass., 1966. MR 34 #5857. MR 0206032 (34:5857)
  • [4] A. Zaks, Algebraic homology, Lecture Notes, Technion-Israel Institute of Technology, Haifa, 1971. (Hebrew)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0338130-9
Keywords: Projective dimension, injective dimension, weak (flat) dimension, projective (injective, flat) resolution, abelian category, derived functor, satellite
Article copyright: © Copyright 1973 American Mathematical Society

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