Balanced and $QF-1$ algebras
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- by V. P. Camillo and K. R. Fuller
- Proc. Amer. Math. Soc. 34 (1972), 373-378
- DOI: https://doi.org/10.1090/S0002-9939-1972-0306256-0
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Abstract:
A ring R is QF-1 if every faithful module has the double centralizer property. It is proved that a local finite dimensional algebra is QF-1 if and only if it is QF. From this it follows that an arbitrary finite dimensional algebra has the property that every homomorphic image is QF-1 if and only if every homomorphic image is QF.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
- 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
- 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
- Carl Faith, A general Wedderburn theorem, Bull. Amer. Math. Soc. 73 (1967), 65–67. MR 202763, DOI 10.1090/S0002-9904-1967-11642-2
- 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
- Kent R. Fuller, Primary rings and double centralizers, Pacific J. Math. 34 (1970), 379–383. MR 271157, DOI 10.2140/pjm.1970.34.379
- J. P. Jans, On the double centralizer condition, Math. Ann. 188 (1970), 85–89. MR 272817, DOI 10.1007/BF01350811
- Kiiti Morita, Duality for modules and its applications to the theory of rings with minimum condition, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 6 (1958), 83–142. MR 96700
- Kiiti Morita, On algebras for which every faithful representation is its own second commutator, Math. Z. 69 (1958), 429–434. MR 126492, DOI 10.1007/BF01187420
- Kiiti Morita, On $S$-rings in the sense of F. Kasch, Nagoya Math. J. 27 (1966), 687–695. MR 199230, DOI 10.1017/S0027763000026477 K. Morita and H. Tachikawa, QF-3 rings (unpublished).
- Tadasi Nakayama, On Frobeniusean algebras. II, Ann. of Math. (2) 42 (1941), 1–21. MR 4237, DOI 10.2307/1968984
- Tadasi Nakayama, Note on uni-serial and generalized uni-serial rings, Proc. Imp. Acad. Tokyo 16 (1940), 285–289. MR 3618
- C. J. Nesbitt and R. M. Thrall, Some ring theorems with applications to modular representations, Ann. of Math. (2) 47 (1946), 551–567. MR 16760, DOI 10.2307/1969092
- 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
- Yasutaka Suzuki, A note on $\textrm {QF}-1$ algebras, Tohoku Math. J. (2) 22 (1970), 225–230. MR 269697, DOI 10.2748/tmj/1178242817
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 373-378
- MSC: Primary 16A36
- DOI: https://doi.org/10.1090/S0002-9939-1972-0306256-0
- MathSciNet review: 0306256