Another Gorenstein analogue of flat modules

作者：Mao, Lixin^*

来源：Communications in Algebra, 2017, 45(10): 4196-4209.

DOI：10.1080/00927872.2016.1245314

• Coherent ring
• glat module
• Gorenstein flat module
• Gorenstein projective module
• precover
• preenvelope

A right R-module M is called glat if any homomorphism from any finitely presented right R-module to M factors through a finitely presented Gorenstein projective right R-module. The concept of glat modules may be viewed as another Gorenstein analogue of flat modules. We first prove that the class of glat right R-modules is closed under direct sums, direct limits, pure quotients and pure submodules for arbitrary ring R. Then we obtain that a right R-module M is glat if and only if M is a direct limit of finitely presented Gorenstein projective right R-modules. In addition, we explore the relationships between glat modules and Gorenstein flat (Gorenstein projective) modules. Finally we investigate the existence of preenvelopes and precovers by glat and finitely presented Gorenstein projective modules.

• 出版日期2017
• 单位南京工程学院