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The Structure of Quasi-Frobenius Rings

Published online by Cambridge University Press:  20 November 2018

Bruno J. Müller
Bruno J. Müller*
Affiliation:
McMaster University, Hamilton, Ontario
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Utilizing a matrix representation of semiperfect rings by a family of bimodules over local rings, we describe the structure of generalized quasi-Frobenius rings in two steps: a cyclic generalized quasi-Frobenius ring is a matrix ring over a cycle of Morita dualities between local rings, and an arbitrary generalized quasi-Frobenius ring is a matrix ring over a family of cyclic generalized quasi-Frobenius rings.

Our results provide a complete classification of generalized quasi-Frobenius rings, modulo the classification of local rings with Morita duality, of certain bimodules over such rings, and of certain rest families of multiplication maps.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1141 - 1151
Copyright
Copyright © Canadian Mathematical Society 1974

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