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Extended semi-hereditary rings

Published online by Cambridge University Press:  09 April 2009

M. W. Evans
M. W. Evans
Affiliation:
84 Glencairn Avenue East Brighton Victoria, Australia
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Abstract

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A ring R for which every finitely generated right submodule of SR, the left flat epimorphic hull of R, is projective is termed an extended semi-hereditary ring. It is shown that several of the characterizing properties of Prufer domains may be generalized to give characterizations of extended semi-hereditary rings. A suitable class of PP rings is introduced which in this case serves as a generalization of commutative integral domains.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 4 , December 1978 , pp. 465 - 474
Copyright
Copyright © Australian Mathematical Society 1978

References

Bergman, G. (1971), ‘Hereditary commutative rings and centres of hereditary rings’, Proc. London Math. Soc. 23, 214–236.CrossRefGoogle Scholar
Bergman, George M. (1972), ‘Hereditarily and co-hereditarily projective modules’, Ring theory, edited by Gordon, R., 257–285 (New York, Academic Press, 1972).Google Scholar
Evans, M. W. (1972), ‘On commutative P.P. rings’, Pacific J. Math. 41, 687–697.CrossRefGoogle Scholar
Evans, M. W. (1977), ‘Extensions of semi-hereditary rings’, J. Austral. Math. Soc. 23, 333–339.CrossRefGoogle Scholar
Goodearl, K. R. (1973), ‘Idealisers and non-singular rings’, Pacific. J Math. 75, 395–402.CrossRefGoogle Scholar
Goodearl, K. R. (1974), ‘Simple self-injective rings need not be Artinian’, Communications in Algebra 2, 83–89.CrossRefGoogle Scholar
Goodearl, K. R. (1975), ‘Subrings of idealiser rings’, J. Algebra 33, 405–429.CrossRefGoogle Scholar
Hattori, Akira (1960), ‘A foundation of torsion theory for modules over general rings’, Nagoya Math. J. 17, 147–158.CrossRefGoogle Scholar
Lambek, Joachim (1966), Lectures on rings and modules (Blaisdell, Waltham, Massachusetts; London; Toronto).Google Scholar
Lambek, Joachim (1971), Torsion theories, additive semantics and rings of quotients (Lecture notes in mathematics, 1977, Springer-Verlag, Berlin, Heidelberg, New York).CrossRefGoogle Scholar
Martindale, Wallace S. III (1973), ‘On semi-prime P.I. rings’, Proc. Amer. Math. Soc. 40, 365–369.CrossRefGoogle Scholar
Robson, J. C. (1972), ‘Idealizers and hereditary Noetherian prime rings’, J. Algebra 22, 45–81.CrossRefGoogle Scholar
Sandomierski, Francis L. (1968), ‘Non-singular rings’, Proc. Amer. Math. Soc. 19, 225–230.CrossRefGoogle Scholar
Small, L. (1967), ‘Semi-Hereditary rings’, Bull. Amer. Math. Soc. 73, 656–658.CrossRefGoogle Scholar
Speed, T. P. (1972), ‘On commutative Baer rings II’, J. Aust. Math. Soc. 13, 1–6.CrossRefGoogle Scholar
Stenström, Bo (1975), Rings of quotients (Springer-verlag, Berlin, Heidelberg, New York).CrossRefGoogle Scholar
Stone, David R. (1970), ‘Torsion-free divisible modules over matrix rings’, Pacific J. Math. 35, 235–253.CrossRefGoogle Scholar