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Quasi-Frobenius X-Rings

Published online by Cambridge University Press:  20 November 2018

Abraham Zaks
Abraham Zaks*
Affiliation:
Technion I.I.T., Haifa, Israel
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In a recent study of a specific class of quasi-Frobenius rings, Feller has found it useful to introduce the X-rings ([3]). He suggested among others the following topics:

  1. (A) Determine the properties of completely indecomposable rings and matrix rings over completely indecomposable rings.

  2. (B) Determine the properties of modules over quasi-Frobenius X-rings.

We point out that the completely indecomposable rings are the local quasi-Frobenius rings. Problems (A) and (B) then lead naturally to semi-local quasi-Frobenius rings, and to matrix algebra over local quasi-Frobenius rings. These types of rings are discussed in sections 1 and 2.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 1 , March 1970 , pp. 23 - 30
Copyright
Copyright © Canadian Mathematical Society 1970

References

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