IJPAM: Volume 59, No. 1 (2010)

SOME NEW LOWER BOUNDS FOR THE NUMBER
OF NEAR-RINGS ON FINITE CYCLIC GROUPS

A.K. Rahnev$^1$, A.A. Golev$^2$
$^{1,2}$Faculty of Mathematics and Informatics
University of Plovdiv
236, Bulgaria Blvd., Plovdiv, 4003, BULGARIA
$^1$e-mail: assen@uni-plovdiv.bg
$^2$e-mail: angelg@uni-plovdiv.bg


Abstract.New lower bounds for the number of the near-rings on finite cyclic groups are obtained. All near-rings on finite cyclic groups of order up to 23 are computed using a new heuristic algorithm. The constructions of more than 98 percents of the zero-symmetric and more than 99.5 percents of the non-zero-symmetric near-rings are described.

Received: January 10, 2010

AMS Subject Classification: 16Y30

Key Words and Phrases: near-ring, finite cyclic group, lower bound

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 59
Issue: 1