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Endomorphisms of the Quasi-Injective Hull of a Module

Published online by Cambridge University Press:  20 November 2018

Edward T. Wong
Edward T. Wong*
Affiliation:
Oberlin College, Oberlin, Ohio
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R is a ring and M is a right R-module for which Rl = {m ∊ M | mR = 0} is the zero submodule. Let and be the injective hull and the quasi-injective hull of M respectively. Then where [1]. The ring plays an important role, in many cases, in the studying of R especially when D is a division ring. For x ∊ M, we denote the annihilator of x in R by xγ = {r ∊ R | xr=0}, whereas xγl={m ∊ M | mxγ=0}. If N is a submodule of M and x ∊ M, x-1(N) is the right ideal in R consisting of elements r in R where xr ∊ N.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 1 , March 1970 , pp. 149 - 150
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Johnson, R. E. and Wong, E. T., Quasi-injective modules and irreducible rings, J. London Math. Soc. 36 (1961), 260-268.Google Scholar