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When N is a left nearring with identity satisfying the descending chain condition on right ideals N can be written as a direct sum of nonzero right ideals that cannot be further decomposed into direct sums of nonzero right ideals. If N is a ring the nature of this decomposition is well understood. A nearring module of N possessing a unique proper nonzero N-subgroup is called a 2-step module. Here we initiate the study of the nature of the previously described decompositions when N is not a ring by considering the situation where N has a faithful 2-step module. [ABSTRACT FROM AUTHOR]

In this paper we study solvability and nilpotency of an expanded group relative to the nearring of zero and congruence preserving functions of the expanded group. A particular case of interest is when the expanded group is a nearring module. This leads to consequences when an expanded group is viewed as a nearring module over its nearring of zero preserving polynomial functions. [ABSTRACT FROM AUTHOR]

If N1 is a nearring, V is a faithful tame N1-module and N2 is a nearring containing N1 such that V is a faithful tame N2-module and the N1- and N2-ideals of V coincide, we study when N1-isomorphic minimal factors of V are N2-isomorphic. We also study a stronger form of such preservation called type preservation. Particular attention is paid to the case where N2 is the nearring of 0-preserving and congruence preserving functions of V , C0(V). Here we will see that isomorphism preservation is related to centralizers of minimal factors relative to C0(V) which then motivates the study of these centralizers as well. [ABSTRACT FROM AUTHOR]