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Finite Direct Sums of Complete Matrix Rings over Perfect Completely Primary Rings

Published online by Cambridge University Press:  20 November 2018

Richard Courter
Richard Courter*
Affiliation:
Wayne State University, Detroit, Michigan
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The main theorem of this paper names seven ring classifications which coincide with the class of rings named in the title. Three of them are (1) rings over which every module is rationally complete, (2) left and right perfect rings over which every module is corationally complete, and (3) right perfect rings over which every right module is rationally complete. Corational completeness (introduced in this paper) and rational completeness are generalizations of projectivity and injectivity, respectively. One recalls that a proper subclass of the rings investigated in this paper, the artinian rings with zero radical, is known to have one-sided characterizations in terms of the injectivity (projectivity) of modules. An example proves, however, that the class of rings over which every right module is rationally complete properly contains the rings of the title.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 430 - 446
Copyright
Copyright © Canadian Mathematical Society 1969

References

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