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Citation - WoS: 5
Citation - Scopus: 3
Rings Over Which Flat Covers of Simple Modules Are Projective
(World Scientific Publishing Co. Pte Ltd, 2012) Büyükaşık, Engin; Büyükaşık, Engin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
Let R be a ring with identity. We prove that, the flat cover of any simple right R-module is projective if and only if R is semilocal and J(R) is cotorsion if and only if R is semilocal and any indecomposable flat right R-module with unique maximal submodule is projective.
Completely Cotorsion Modules
(Publishing House of the Bulgarian Academy of Sciences, 2012) Pusat, Dilek; Pusat, Dilek; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We show that any finitely generated projective cotorsion left module over a ring of left pure global dimension at most 1 is a direct sum of indecomposable direct summands. We deduce that such a ring is left cotorsion and semiperfect if and only if its left cotorsion envelope is finitely presented. Some extensions of this result are also discussed.

Mathematics / Matematik