Semidistributive nearrings with identity
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 nearring $R$ actually is an associative ring.
math.RA↗
arXiv subjects
Iryna Raievska
Publications and source records attributed to Iryna Raievska.
Groups of the nilpotency class $3$ of order $p^4$ as additive groups of local nearrings
We consider groups of the nilpotency class $3$ of order $p^4$ which are the additive groups of local nearrings. It was shown that, for $p>3$, there exist a local nearring on one of such 4 groups.
math.GR↗
Lower bounds for the number of local nearrings on groups of order $p^3$
Lower bounds for the number of local nearrings on groups of order $p^3$ are obtained. On each non-metacyclic non-abelian or metacyclic abelian groups of order $p^3$ there exist at least $p+1$ non-isomorphic local nearrings
math.RA↗
Groups of the nilpotency class $2$ of order $p^4$ as additive groups of local nearrings
We consider groups of the nilpotency class $2$ of order $p^4$ which are the additive groups of local nearrings. It was shown that, for odd p, out of 6 of such groups 4 of them are the additive groups of local nearrings. Some examples of such nearrings are explicitly constructed.
math.RA↗