We consider a small category naturally associated with any fixed R-S-bimodule MSR. The class of objects of this category is the underlying set M of MSR. Some additive decompositions of the elements of the bimodule MSR appear naturally. They are the analog of the usual decompositions of the identity 1R of a ring R as sums of pairwise orthogonal idempotents. We extend results by Campanini, El-Deken and Facchini from the category Morph(Mod-R) of all morphisms in the category Mod-R to arbitrary bimodules MSR.
Some natural additive decompositions of elements in bimodules
Facchini A.
;
2022
Abstract
We consider a small category naturally associated with any fixed R-S-bimodule MSR. The class of objects of this category is the underlying set M of MSR. Some additive decompositions of the elements of the bimodule MSR appear naturally. They are the analog of the usual decompositions of the identity 1R of a ring R as sums of pairwise orthogonal idempotents. We extend results by Campanini, El-Deken and Facchini from the category Morph(Mod-R) of all morphisms in the category Mod-R to arbitrary bimodules MSR.File in questo prodotto:
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