## Taiwanese Journal of Mathematics

### $0$-PRIMITIVE NEAR-RINGS, MINIMAL IDEALS AND SIMPLE NEAR-RINGS

Gerhard Wendt

#### 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.

#### Article information

Source
Taiwanese J. Math., Volume 19, Number 3 (2015), 875-905.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133667

Digital Object Identifier
doi:10.11650/tjm.19.2015.5077

Mathematical Reviews number (MathSciNet)
MR3353258

Zentralblatt MATH identifier
1357.16063

Subjects

#### Citation

Wendt, Gerhard. $0$-PRIMITIVE NEAR-RINGS, MINIMAL IDEALS AND SIMPLE NEAR-RINGS. Taiwanese J. Math. 19 (2015), no. 3, 875--905. doi:10.11650/tjm.19.2015.5077. https://projecteuclid.org/euclid.twjm/1499133667

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