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On Extensions of Weakly Primitive Rings

Published online by Cambridge University Press:  20 November 2018

W. K. Nicholson ,
J. F. Waiters  and
J. M. Zelmanowitz
W. K. Nicholson
Affiliation:
University of Calgary, Calgary, Alberta
J. F. Waiters
Affiliation:
University of Leicester, Leicester, England
J. M. Zelmanowitz
Affiliation:
University of California, Santa Barbara, California
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If R is a ring an R-module M is called compressible when it can be embedded in each of its non-zero submodules; and M is called monoform if each partial endomorphism N → M, N ⊆ M, is either zero or monic. The ring R is called (left) weakly primitive if it has a faithful monoform compressible left module. It is known that a version of the Jacobson density theorem holds for weakly primitive rings [4], and that weak primitivity is a Mori ta invariant and is inherited by a variety of subrings and matrix rings. The purpose of this paper is to show that weak primitivity is preserved under formation of polynomials, rings of quotients, and group rings of torsion-free abelian groups. The key result is that R[x] is weakly primitive when R is (Theorem 1).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 4 , April 1980 , pp. 937 - 944
Copyright
Copyright © Canadian Mathematical Society 1980

References

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4. Zelmanowitz, J., Dense rings of linear transformations, Ring Theory II, Proceedings of the Second Oklahoma Conference (Marcel Dekker, New York, 1977).Google Scholar