## nil-injective rings.(English)Zbl 1123.16003

Summary: A ring $$R$$ is called left nil-injective if every $$R$$-homomorphism from a principal left ideal which is generated by a nilpotent element to $$R$$ is a right multiplication by an element of $$R$$. In this paper, we first introduce and characterize a left nil-injective ring, which is a proper generalization of left p-injective rings. Next, various properties of left nil-injective rings are developed, many of them extend known results.

### MSC:

 16D50 Injective modules, self-injective associative rings 16N40 Nil and nilpotent radicals, sets, ideals, associative rings 16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
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