Natural Classes,Left Exact Preradicals,and Flat Epimorphisms |
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Abstract: | We define a function between the lattice of left exact preradicals in R-mod and the complete boolean lattice R-nat of natural classes in R-mod in such a way that the image of this function results to be a complete sublattice of R-nat. The image of this function is R-nat if and only if R is left semiartinian. We prove that every flat ring epimorphism from R to S induces a function between the lattice of left exact preradicals in R-mod and the lattice of left exact preradicals in S-mod. In this context, we obtain a lattice decomposition of S-nat for each left exact preradical. |
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Keywords: | Natural class Left exact preradical Flat epimorphism |
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