Abstract
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.
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