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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
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] Maurice Auslander and Mark Bridger, Stable module theory, Memoirs of the American Mathematical Society, No. 94, American Mathematical Society, Providence, R.I., 1969. MR 0269685
  • [2] Irving Kaplansky, Commutative rings, Allyn and Bacon, Inc., Boston, Mass., 1970. MR 0254021
  • [3] Joachim Lambek, Lectures on rings and modules, With an appendix by Ian G. Connell, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. MR 0206032
  • [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