Commutative $\textrm {QF}-1$ rings
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- by Claus Michael Ringel
- Proc. Amer. Math. Soc. 42 (1974), 365-368
- DOI: https://doi.org/10.1090/S0002-9939-1974-0344283-X
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Abstract:
If R is a commutative artinian ring, then it is known that every faithful R-module is balanced (i.e. has the double centralizer property) if and only if R is a quasi-Frobenius ring. In this note it is shown that the assumption on R to be artinian can be replaced by the weaker condition that R is noetherian.References
- Victor P. Camillo, Balanced rings and a problem of Thrall, Trans. Amer. Math. Soc. 149 (1970), 143–153. MR 260794, DOI 10.1090/S0002-9947-1970-0260794-0
- S. E. Dickson and K. R. Fuller, Commutative $\textrm {QF}-1$ artinian rings are $\textrm {QF}$, Proc. Amer. Math. Soc. 24 (1970), 667–670. MR 252426, DOI 10.1090/S0002-9939-1970-0252426-8
- N. J. Divinsky, Commutative subdirectly irreducible rings, Proc. Amer. Math. Soc. 8 (1957), 642–648. MR 86799, DOI 10.1090/S0002-9939-1957-0086799-X
- Vlastimil Dlab and Claus Michael Ringel, Balanced rings, 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. 73–143. MR 0340344
- Denis Ragan Floyd, On $\textrm {QF}-1$ algebras, Pacific J. Math. 27 (1968), 81–94. MR 234988
- R. M. Thrall, Some generalization of quasi-Frobenius algebras, Trans. Amer. Math. Soc. 64 (1948), 173–183. MR 26048, DOI 10.1090/S0002-9947-1948-0026048-0
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 365-368
- MSC: Primary 16A36
- DOI: https://doi.org/10.1090/S0002-9939-1974-0344283-X
- MathSciNet review: 0344283