Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

On splitting cotorsion radicals


Author: V. S. Ramamurthi
Journal: Proc. Amer. Math. Soc. 39 (1973), 457-461
MSC: Primary 16A62
DOI: https://doi.org/10.1090/S0002-9939-1973-0313323-5
MathSciNet review: 0313323
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For a category of modules, the notion, dual to that of a torsion radical, has been called a cotorsion radical. In this paper, the following two properties are examined for a cotorsion radical $ \rho $: (1) If $ N$ is a submodule of $ M$ and $ \rho (M) = M$, then $ \rho (N) = N$. (2) The exact sequence $ 0 \to \rho (M) \to M \to M/\rho (M) \to 0$ splits for each module $ M$.


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

  • [1] H. Bass, Finististic dimension and a homological generalisation of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488. MR 28 #1212. MR 0157984 (28:1212)
  • [2] J. A. Beachy, Cotorsion radicals and projective modules, Bull. Austral. Math. Soc. 5 (1971), 241-253. MR 0292879 (45:1961)
  • [3] R. L. Bernhardt, Splitting hereditary torsion theories over semiperfect rings, Proc. Amer. Math. Soc. 22 (1969), 681-687. MR 39 #5639. MR 0244324 (39:5639)
  • [4] S. U. Chase, Direct product of modules, Trans. Amer. Math. Soc. 97 (1960), 457-473. MR 22 #11017. MR 0120260 (22:11017)
  • [5] S. E. Dickson, A torsion theory for abelian categories, Trans. Amer. Math. Soc. 121 (1966), 223-235. MR 33 #162. MR 0191935 (33:162)
  • [6] C. Faith, Modules finite over endomorphism ring, Lecture Notes in Math., no. 246, Springer-Verlag, Berlin, 1972, pp. 146-190. MR 0342541 (49:7287)
  • [7] A. W. Goldie, Semi-prime rings with maximum condition, Proc. London. Math. Soc. (3) 10 (1960), 201-220. MR 22 #2627. MR 0111766 (22:2627)
  • [8] J. P. Jans, Rings and homology, Holt, Rinehart and Winston, New York, 1964. MR 29 #1243. MR 0163944 (29:1243)
  • [9] J. Lambek, Lectures on rings and modules, Blaisdell, Waltham, Mass., 1966. MR 34 #5857. MR 0206032 (34:5857)
  • [10] J. M. Maranda, Injective structures, Trans. Amer. Math. Soc. 110 (1964), 98-135. MR 29 #1236. MR 0163937 (29:1236)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A62

Retrieve articles in all journals with MSC: 16A62


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0313323-5
Keywords: Torsion radical, cotorsion radical, flat modules, von Neumann regular rings, semiperfect rings, quasi-Frobenius ring
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society