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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Modules satisfying both chain conditions with respect to a torsion theory
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by Jonathan S. Golan PDF
Proc. Amer. Math. Soc. 52 (1975), 103-108 Request permission

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
  • Jonathan S. Golan, Topologies on the torsion-theoretic spectrum of a noncommutative ring, Pacific J. Math. 51 (1974), 439–450. MR 369439
  • Oscar Goldman, Rings and modules of quotients, J. Algebra 13 (1969), 10–47. MR 245608, DOI 10.1016/0021-8693(69)90004-0
  • —, Elements of non-commutative arithmetic. I, 1974 (preprint).
  • Joachim Lambek, Torsion theories, additive semantics, and rings of quotients, Lecture Notes in Mathematics, Vol. 177, Springer-Verlag, Berlin-New York, 1971. With an appendix by H. H. Storrer on torsion theories and dominant dimensions. MR 0284459
  • J. N. Manocha, Finiteness conditions and torsion theories. I, 1974 (preprint).
  • J. Raynaud, Localisations et anneaux semi-noéthériens à droite, Publ. Dép. Math. (Lyon) 8 (1971), no. 3-4, 77–112 (French). MR 335561
  • Bo Stenström, Rings and modules of quotients, Lecture Notes in Mathematics, Vol. 237, Springer-Verlag, Berlin-New York, 1971. MR 0325663
  • Hans H. Storrer, On Goldman’s primary decomposition, Lectures on rings and modules (Tulane Univ. Ring and Operator Theory Year, 1970–1971, Vol. I), Lecture Notes in Math., Vol. 246, Springer, Berlin, 1972, pp. 617–661. MR 0360717
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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