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RESEARCH PRODUCT

Local nearrings with dihedral multiplicative group

Yaroslav P. SysakBernhard AmbergPeter Hubert

subject

Local nearringAlgebra and Number TheoryDicyclic groupMultiplicative groupDihedral angleCombinatoricsDihedral groupOrder (group theory)Element (category theory)Factorized groupDihedral group of order 6Unit (ring theory)Additive groupMathematics

description

AbstractA not necessarily zero-symmetric nearring R with a unit element is called local if the set of all non-invertible elements of R forms a subgroup of the additive group of R. It is proved that every local nearring whose multiplicative group is dihedral is finite and its additive group is either a 3-group of order at most 9 or a 2-group of order at most 32.

yearjournalcountryeditionlanguage
2004-03-01Journal of Algebra
10.1016/j.jalgebra.2003.10.007http://dx.doi.org/10.1016/j.jalgebra.2003.10.007