Distribution and generalized centre in planar nearrings

Boykett Tim: Distribution and generalized centre in planar nearrings. In: Acta scientiarum mathematicarum 86. pp. 11-29. (2020)

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Abstract

Nearrings are the nonlinear generalization of rings. Planar nearrings play an important role in nearring theory, both from the structural side, being close to generalized nearfields, as well as from an applications perspective, in geometry and combinatorial designs related to difference families. In this paper we investigate the distributive elements of planar nearrings. If a planar nearring has nonzero distributive elements, then it is an extension of an abelian group by its zero multiplier part. In the case that there are distributive elements that are not zero multipliers, then this extension splits, giving an explicit description of the nearring, a coordinatisation result. This generalizes the structure of planar rings. We provide a family of examples where this does not occur, the distributive elements being precisely the zero multipliers. We apply this knowledge to the question of determining the generalized centre of planar nearrings as well as finding new proofs of older results.

Item Type:	Article
Heading title:	Algebra
Journal or Publication Title:	Acta scientiarum mathematicarum
Date:	2020
Number:	86
ISSN:	2064-8316
Page Range:	pp. 11-29
Related URLs:	http://acta.bibl.u-szeged.hu/69543/
DOI:	10.14232/actasm-018-036-y
Uncontrolled Keywords:	Matematika, Algebra
Additional Information:	Bibliogr.: p. 27-29. ; összefoglalás angol nyelven
Subjects:	01. Natural sciences 01. Natural sciences > 01.01. Mathematics
Date Deposited:	2020. Jul. 27. 09:34
Last Modified:	2020. Jul. 27. 09:34
URI:	http://acta.bibl.u-szeged.hu/id/eprint/69360

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