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On Injective Near-Ring Modules

Published online by Cambridge University Press:  20 November 2018

V. Seth  and
K. Tewari
V. Seth
Affiliation:
Indian Institute of Technology, Kanpur, India
K. Tewari
Affiliation:
Indian Institute of Technology, Kanpur, India
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Let N be a left near ring and let M be a right N-module. We recall [1] that M is called injective iff every diagram can be embedded into a commutative diagram where A and B are right N-modules with exact.

The purpose of this note is to show that if N is a d.g. near-ring with identity, then M is injective iff for every right ideal u of N and every N-homomorphism f:u→N, there exists an element m in M such that f(a)=ma for all a in u.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 137 - 141
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Maxson, Carlton J., Dickson near-rings, J. Algebra 14 (1970), 152-169.Google Scholar
2. Beidleman, J. C., Quasi-regularity in near-rings, Math, Z. 89 (1965), 224-229.Google Scholar