ANNA BENINI and SILVIA PELLEGRINI

Finite weakly divisible nearrings

Pages 101-116
Received: 28 May 2009   
Accepted in revised form: 26 August 2009
Mathematics Subject Classification (2000): 16Y30

Keywords: Near-rings.

This research was partially supported by italian MIUR.

Abstract In [5] the algebraic structure called weakly divisible nearring (wd-nearring) was defined and studied. In [1, 2] a special class of wd-nearrings was constructed and its combinatorial properties was investigated. In [3] PBIBDs were derived from a class of wd-nearrings and their parameters were calculated thanks to the knowledge of the algebraic structure. In [9] a generalization of the construction of [1, 2] was given. In order to generalize the construction of [3] to more general cases, this paper is devoted to a more in depth study of the algebraic structure of any finite wd-nearring N, especially with regard to determining the size of the elements of significant structures in N, as partitions, normal chains and products.