Commutative $\textrm {QF}-1$ artinian rings are $\textrm {QF}$
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- by S. E. Dickson and K. R. Fuller
- Proc. Amer. Math. Soc. 24 (1970), 667-670
- DOI: https://doi.org/10.1090/S0002-9939-1970-0252426-8
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Abstract:
In a recent paper, D. R. Floyd proved several results on algebras, each of whose faithful representations is its own bicommutant ( = R. M. Thrall’s ${\text {QF - }}1$ algebras, a generalization of ${\text {QF}}$-algebras) among which was the theorem in the title for algebras. We obtain our extension of Floyd’s result by use of interlacing modules, replacing his arguments involving the representations themselves.References
- R. R. Colby and E. A. Rutter, Jr., A remark concerning ${\text {QF - }}3$ rings, (to appear).
- Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0144979
- Spencer E. Dickson, On algebras of finite representation type, Trans. Amer. Math. Soc. 135 (1969), 127–141. MR 237558, DOI 10.1090/S0002-9947-1969-0237558-9
- Denis Ragan Floyd, On $\textrm {QF}-1$ algebras, Pacific J. Math. 27 (1968), 81–94. MR 234988, DOI 10.2140/pjm.1968.27.81
- Kent R. Fuller, Generalized uniserial rings and their Kupisch series, Math. Z. 106 (1968), 248–260. MR 232795, DOI 10.1007/BF01110273
- Nathan Jacobson, The Theory of Rings, American Mathematical Society Mathematical Surveys, Vol. II, American Mathematical Society, New York, 1943. MR 0008601, DOI 10.1090/surv/002
- J. P. Jans, Note on $\textrm {QF}$-$1$ algebras, Proc. Amer. Math. Soc. 20 (1969), 225–228. MR 233848, DOI 10.1090/S0002-9939-1969-0233848-X
- Bruno J. Müller, Dominant dimension of semi-primary rings, J. Reine Angew. Math. 232 (1968), 173–179. MR 233854, DOI 10.1515/crll.1968.232.173
- Tadasi Nakayama, On Frobeniusean algebras. II, Ann. of Math. (2) 42 (1941), 1–21. MR 4237, DOI 10.2307/1968984
- 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 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 24 (1970), 667-670
- MSC: Primary 16.25
- DOI: https://doi.org/10.1090/S0002-9939-1970-0252426-8
- MathSciNet review: 0252426