Abstract
A faithful compatible module G of a nearring R is 1-affine complete if R equals the set of congruence preserving functions of G that are 0-preserving. The study of 1-affine complete expanded groups G can be approached from this perspective by considering G as a module for the nearring of 0-preserving polynomial functions of G. In this paper, we obtain some strong conditions on the minimal R-ideals of G, when R has dccr and G is 1-affine complete, by using results from papers on units of such nearrings. We then go on to apply these results to obtain necessary and sufficient conditions for G to have a composition series in which each factor of G by a series term is 1-affine complete.
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11 October 2017
We correct a theorem in the original paper concerning when a composition series of a compatible nearring module is a 1-affine complete chain.
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Portions of this paper were developed while the author was a guest of Johannes Kepler Universität in Linz, Austria in July, 2013 partially supported by the Austrian Science Fund (FWF): P24077. The author thanks the University for its hospitality and support through this grant during this time.
An erratum to this article is available at https://doi.org/10.1007/s00012-017-0458-8.
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Peterson, G.L. 1-affine completeness of compatible modules. Algebra Univers. 76, 99–110 (2016). https://doi.org/10.1007/s00012-016-0385-0
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DOI: https://doi.org/10.1007/s00012-016-0385-0