Commutative $\textrm {QF}-1$ artinian rings are $\textrm {QF}$
Authors:
S. E. Dickson and K. R. Fuller
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
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Abstract | References | Similar Articles | Additional Information
Abstract: In a recent paper, D. R. Floyd proved several results on algebras, each of whose faithful representations is its own bicommutant ( = R. M. Thrallโs ${\text {QF - }}1$ algebras, a generalization of ${\text {QF}}$-algebras) among which was the theorem in the title for algebras. We obtain our extension of Floydโs result by use of interlacing modules, replacing his arguments involving the representations themselves.
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R. R. Colby and E. A. Rutter, Jr., A remark concerning ${\text {QF - }}3$ rings, (to appear).
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Keywords:
<!โ MATH ${\text {QF - }}1$ โ> <IMG WIDTH="64" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="${\text {QF - }}1$"> ring,
<!โ MATH ${\text {QF}}$ โ> <IMG WIDTH="34" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${\text {QF}}$">-ring,
Frobenius ring,
quasi-Frobenius ring,
artinian ring,
faithful module,
bicommutant,
double centralizer property
Article copyright:
© Copyright 1970
American Mathematical Society