Dergi makalesi Açık Erişim

ABSOLUTELY s-PURE MODULES AND NEAT-FLAT MODULES

Buyukasik, Engin; Durgun, Yilmaz


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        "affiliation": "Izmir Inst Technol, Dept Math, TR-35430 Izmir, Turkey", 
        "name": "Buyukasik, Engin"
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        "affiliation": "Izmir Inst Technol, Dept Math, TR-35430 Izmir, Turkey", 
        "name": "Durgun, Yilmaz"
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    "description": "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.", 
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