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Proceedings of the American Mathematical Society

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

 

 

Modules satisfying both chain conditions with respect to a torsion theory


Author: Jonathan S. Golan
Journal: Proc. Amer. Math. Soc. 52 (1975), 103-108
MSC: Primary 16A46
DOI: https://doi.org/10.1090/S0002-9939-1975-0429981-2
MathSciNet review: 0429981
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Abstract: Goldman [3] has introduced the notion of the length of a module with respect to a torsion theory and has studied finitely-generated modules over left noetherian rings which have finite length. In this note we simplify the proofs of some of Goldman's results and generalize them by removing both the finite-generation and noetherianness conditions.


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

  • [1] Jonathan S. Golan, Topologies on the torsion-theoretic spectrum of a noncommutative ring, Pacific J. Math. 51 (1974), 439–450. MR 0369439
  • [2] Oscar Goldman, Rings and modules of quotients, J. Algebra 13 (1969), 10–47. MR 0245608, https://doi.org/10.1016/0021-8693(69)90004-0
  • [3] -, Elements of non-commutative arithmetic. I, 1974 (preprint).
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  • [7] Bo Stenström, Rings and modules of quotients, Lecture Notes in Mathematics, Vol. 237, Springer-Verlag, Berlin-New York, 1971. MR 0325663
  • [8] Hans H. Storrer, On Goldman’s primary decomposition, Lecutres on rings and modules (Tulane Univ. Ring and Operator Theory Year, 1970–1971, Vol. I), Springer, Berlin, 1972, pp. 617–661. Lecture Notes in Math., Vol. 246. MR 0360717

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0429981-2
Article copyright: © Copyright 1975 American Mathematical Society