nil-injective rings. (English) Zbl 1123.16003

Wei, Junchao; Chen, Jinhua

Int. Electron. J. Algebra 2, 1-21 (2007).

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)

Keywords:

left minimal elements; left MC2 rings; simple singular modules; left nil-injective modules; nilpotent elements; right multiplications; left p-injective rings