Abstract
If R is a zero-symmetric nearring with 1 and G is a faithful R-module, a compatible extension of R is a subnearring S of M 0(G) containing R such that G is a compatible S-module and the R-ideals and S-ideals of G coincide. The set of these compatible extensions forms a complete lattice and we shall study this lattice. We also will obtain results involving the least element of this lattice related to centralizers and the largest element of this lattice related to uniqueness of minimal factors with an application to 1-affine completeness of the R-module G.
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Peterson, G.L. Compatible extensions of nearrings. Monatsh Math 161, 399–415 (2010). https://doi.org/10.1007/s00605-009-0139-6
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DOI: https://doi.org/10.1007/s00605-009-0139-6