Centre for Interdisciplinary Research in Computational Algebra (CIRCA) seminar Iryna Raievska and Maryna Raievska

Iryna Raievska and Maryna Raievska, Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine, will present Local nearrings and GAP package LocalNR (Part 2)

Abstract: Nearrings naturally arise in the study of systems of nonlinear mappings, and have been studied for many decades. Nearrings are generalized rings in the sense that the addition need not be commutative and only one distributive law is assumed. Clearly every associative ring is a nearring and each group is the additive group of a nearring, but not necessarily of a nearring with identity. The question of what group can be the additive group of a nearring with identity is far from solution.

The LocalNR package contains the library of local nearrings up to order 361 and some functions to analyze finite nearrings.

Using GAP we study local nearrings with some restrictions on multiplicative groups, additive groups and subgroups of non-invertible elements, and related structures.

More information is available at https://circa.st-andrews.ac.uk/news/