Semidistributive nearrings with identity

Author:

,Raievska Iryna,Raievska Maryna, ,Sysak Yaroslav,

Abstract

It is proved that the additive group of every semidistributive nearring R with an identity is abelian and if R has no elements of order 2, then the nearringRactually is anassociative ring.

Publisher

Luhansk Taras Shevchenko National University

Reference5 articles.

1. [1] J.R. Clay, Jr. Malone,The near-rings with identities on certain finite groups, Math.Scand.,19, 1966, pp. 146-150.

2. [2] The GAP Group,GAP - Groups, Algorithms, and Programming, Version 4.10.2,2019 (https://www.gap-system.org).

3. [3] J.D.P. Meldrum,Near-rings and their links with groups, Pitman Publishing Limi-ted, London, 1985, 273 p.

4. [4] G. Pilz,Near-rings. The theory and its applications, North Holland, Amsterdam,1977.

5. [5] E. Aichinger, F. Binder, Ju. Ecker, P. Mayr and C. Noebauer,SONATA -system of near-rings and their applications, GAP package, Version 2.9.1, 2018(https://gap-packages.github.io/sonata/).

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