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TTF-classes over perfect rings

Published online by Cambridge University Press:  09 April 2009

J. S. Alin  and
E. P. Armendariz
J. S. Alin
Affiliation:
The University of Utah, Salt Lake City, Utah
E. P. Armendariz
Affiliation:
The University of Texas, Austin, Texas
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For a ring R with unit, let RM denote the category of unitary left R-modules. Following S.E. Dickson [3], a(non-empty) class of R-modules is a torsion class in rM if is closed under factors, extensions, and direct sums. If, in addition, is closed under submodules, then is said to be hereditary.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 4 , November 1970 , pp. 499 - 503
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Alin, J. S. and Dickson, S. E., ‘Goldie's torsion theory and its derived functor’, Pacific J. Math. 24 (1968), 195–203.CrossRefGoogle Scholar
[2]Bass, H., ‘Finitistic dimension and a homological generalization of semi-primary rings’, Trans. Amer. Math. Soc. 95 (1960), 466–488.CrossRefGoogle Scholar
[3]Dickson, S. E., ‘A torsion theory for Abelian categories’ Trans. Amer. Math. Soc. 121 (1966), 223–235.CrossRefGoogle Scholar
[4]Dickson, S. E., ‘Decomposition of Modules I. Classical rings’, Math. Z. 90 (1965), 9–13CrossRefGoogle Scholar
[5]Dlab, V., ‘The concept of a torsion module’, Amer. Math. Monthly 75 (1968), 973–976.Google Scholar
[6]Eckmann, B. and Schopf, A., ‘Über injective Modulen’, Archiv der Math. 4 (1953), 75–78.CrossRefGoogle Scholar
[7]Goldie, A. W., ‘Torsion free modules and rings’, J. Algebra 1 (1964), 268–287.CrossRefGoogle Scholar
[8]Gentile, E., ‘Singular submodule and injective hull’, Indag. Math. 24 (1962), 426–433.CrossRefGoogle Scholar
[9]Jans, J. P., ‘Some aspects of torsion’, Pacific J. Math. 15 (1965), 1249–1259.CrossRefGoogle Scholar
[10]Johnson, R. E., ‘The extended centralizer of a ring over a module’, Proc. Amer. Math. Soc. 2 (1951), 891–895.CrossRefGoogle Scholar
[11]Pierce, R. S., Modules over Commutative Regular Rings (Memoirs Amer. Math. Soc. 70, Providence, R. I., 1967).Google Scholar