ABSOLUTELY s-PURE MODULES AND NEAT-FLAT MODULES

作者：Buyukasik Engin; Durgun Yilmaz^*

来源：Communications in Algebra, 2015, 43(2): 384-399.

DOI：10.1080/00927872.2013.842246

• Absolutely s-pure module
• Injective cover
• Kasch ring
• Neat submodule
• Simple-projective module
• s-Pure submodule

Let R be a ring with an identity element. We prove that R is right Kasch if and only if injective hull of every simple right R-modules is neat-flat if and only if every absolutely pure right R-module is neat-flat. A commutative ring R is hereditary and noetherian if and only if every absolutely s-pure R-module is injective and R is nonsingular. If every simple right R-module is finitely presented, then (1) R-R is absolutely s-pure if and only if R is right Kasch and (2) R is a right Sigma-CS ring if and only if every pure injective neat-flat right R-module is projective if and only if every absolutely s-pure left R-module is injective and R is right perfect. We also study enveloping and covering properties of absolutely s-pure and neat-flat modules. The rings over which every simple module has an injective cover are characterized.

• 出版日期2015