
ZWGPinjectivity and nonsingularity of rings
 LU Qi, BAO Hongwei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2):
1923.
doi:10.6040/j.issn.16719352.0.2016.173

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ZWGPinjective modules and ZWGPinjective rings are introduced; equivalent characterizations of ZWGPinjective rings are obtained. The properties of ZWGPinjective modules(rings)are explored, the relations between ZWGPinjective rings and nonsingular rings are illustrated by some examples, and sufficient and necessary conditions that rings are nonsingular are given. It is proved that:(1)If left annihilators of R are Wideals of R, and any essential ideals of R are left ZWGPinjective, then R is left nonsingular;(2)If for any essential left ideal I,R/I is ZWGPinjective, and l(a_{}1)⊆l(a_{}1a_{}2)⊆l(a_{}1a_{}2a_{}3)⊆… is stable, a_{i}∈Z(_{R}R), i=1,2,3,…, then R is left nonsingular.