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Minimal left ideals of near-rings. (English) Zbl 1259.16051

Summary: We show that a finite minimal left ideal \(L\) of a zero symmetric near-ring \(N\) is a planar near-ring if \(L\) is not contained in the radical \(J_2(N)\). This result will follow from a more general discussion on minimal \(N\)-subgroups of a near-ring. Then we discuss some consequences of this result when applied to the structure theory of near-rings. Finally we transfer our results to rings and deal with some ring theoretic questions concerning “trivial” multiplications in rings.

MSC:

16Y30 Near-rings
16D25 Ideals in associative algebras

Software:

SONATA
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Full Text: DOI

References:

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