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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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