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QF - 1 Rings of Global Dimension ≦ 2

Published online by Cambridge University Press:  20 November 2018

Claus Michael Ringel
Claus Michael Ringel*
Affiliation:
Mathematisches Institut der Universität, Tubingen, Germany; Carleton University, Ottawa, Ontario
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R. M. Thrall [10] introduced QF — 1, QF — 2 and QF — 3 rings as generalizations of quasi-Frobenius rings. (For definitions, see section 1. It should be noted that all rings considered are assumed to be left and right artinian.) He proved that QF — 2 rings are QF — 3 and asked whether all QF — 1 rings are QF — 2, or, at least, QF — 3. In [9] we have shown that QF — 1 rings are very similar to QF — 3 rings. On the other hand, K. Morita [6] gave two examples of QF — 1 rings, one of them not QF — 2 and therefore not QF — 3, the other one QF — 3, but not QF — 2.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 2 , April 1973 , pp. 345 - 352
Copyright
Copyright © Canadian Mathematical Society 1973

References

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