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Title: Absolutely s-pure modules and neat-flat modules
Authors: Büyükaşık, Engin
Durğun, Yılmaz
Büyükaşık, Engin
Durğun, Yılmaz
Izmir Institute of Technology. Mathematics
Keywords: Absolutely s-pure module
Injective cover
Kasch ring
Neat submodule
Modules (Algebra)
Issue Date: Feb-2015
Publisher: Taylor and Francis Ltd.
Source: Büyükaşık, E., and Durğun, Y. (2015). Absolutely s-pure modules and neat-flat modules. Communications in Algebra, 43(2), 384-399. doi:10.1080/00927872.2013.842246
Abstract: 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 (Formula presented.) -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. © 2015 Taylor & Francis Group, LLC.
ISSN: 0092-7872
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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