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Injective endomorphisms and maximal left ideals of left Artinian rings

Published online by Cambridge University Press:  18 May 2009

J. C. Wilkinson
J. C. Wilkinson
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL
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Given a ring R and an injective ring endomorphism α: R → R, not necessarily surjective, it is possible to define a minimal overring A(R, α) of R to which extends as an automorphism. The ring A(R, α) was first studied by D. A. Jordan in his paper [5], where he also introduces the central objects of this paper—the closed left ideals of R. As can be seen from Theorem 4.7 of [5], the left ideal structure of A(R, α) depends very strongly on the closed left ideals of R, and our aim here is to show that each maximal left ideal of a left Artinian ring is closed.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 2 , May 1988 , pp. 195 - 201
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

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