International Journal of Pure and Applied Mathematics Volume 90 No. 3 2014, 345-356 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v90i3.8 P A ijpam.eu DISTRIBUTED SOFTWARE SYSTEM FOR TESTING NEAR-RINGS HYPOTHESES AND NEW CONSTRUCTIONS FOR NEAR-RINGS ON FINITE CYCLIC GROUPS N. Pavlov 1 , A. Golev 2 , A. Rahnev 3 § 1,2,3 Faculty of Mathematics and Informatics University of Plovdiv 236, Bulgaria Blvd., 4003, Plovdiv, BULGARIA Abstract: In this paper we describe a software system for testing hypothe- ses about near-rings on finite cyclic groups. The system allows researchers to define parameters and test π functions. By using this software we make new hy- potheses, and formulate and prove statements for constructions of new classes of near-rings. We compute all near-rings on finite cyclic group of order 33, 34 and 35. AMS Subject Classification: 16Y30 Key Words: near-ring, finite cyclic group, distributed software, grid com- puting 1. Introduction An algebraic system (G, +, ∗) is a (left) near-ring on (G, +) if (G, +) is a group, (G, ∗) is a semigroup and a ∗ (b + c)= a ∗ b + a ∗ c for a, b, c ∈ G. The left Received: September 11, 2013 c  2014 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author