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2015 $0$-PRIMITIVE NEAR-RINGS, MINIMAL IDEALS AND SIMPLE NEAR-RINGS
Gerhard Wendt
Taiwanese J. Math. 19(3): 875-905 (2015). DOI: 10.11650/tjm.19.2015.5077

Abstract

We study the structure of $0$-primitive near-rings and are able to answer an open question in the theory of minimal ideals in near-rings to the negative, namely if the heart of a zero symmetric subdirectly irreducible near-ring is subdirectly irreducible again. Also, we will be able to classify when a simple near-ring with an identity and containing a minimal left ideal is a Jacobson radical near-ring. Such near-rings are known to exist but have unusual properties. Along the way we prove results on minimal ideals and left ideals in near-rings which so far were known to hold or have been established in the DCCN case, only.

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Gerhard Wendt. "$0$-PRIMITIVE NEAR-RINGS, MINIMAL IDEALS AND SIMPLE NEAR-RINGS." Taiwanese J. Math. 19 (3) 875 - 905, 2015. https://doi.org/10.11650/tjm.19.2015.5077

Information

Published: 2015
First available in Project Euclid: 4 July 2017

zbMATH: 1357.16063
MathSciNet: MR3353258
Digital Object Identifier: 10.11650/tjm.19.2015.5077

Subjects:
Primary: 16Y30

Keywords: left ideals , minimal ideals , primitive near-rings , simple near-rings , subdirectly irreducible near-rings

Rights: Copyright © 2015 The Mathematical Society of the Republic of China

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Vol.19 • No. 3 • 2015
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