We know that the Gorenstein projectivity relative to a semidualizing module is preserved under excellent extensions. A new method of proof is adopted when the conclusion is known to be correct. Using the equivalent proposition of the definition to prove that for an excellent extension R→S and an S-module SM,RMisGCprojective module if and only ifSM isGSRCprojective module. The form of the new method after using equivalent proposition is uniform. It is convenient to generalize and apply the related properties of modules.
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周珺,胡月,葛茂荣.优越扩张下GC--投射模[J].重庆工商大学学报(自然科学版),2020,37(5):43-46 ZHOU Jun, HU Yue, GE Mao-rong. GC-projective Modules under Excellence Extension[J]. Journal of Chongqing Technology and Business University(Natural Science Edition),2020,37(5):43-46