arXiv subjects
Publications and source records attributed to Pınar Aydoğdu.
We construct a family of semiprimitive and non von Neumann regular rings satisfying that any right or left module is isomorphic to a quotient of its flat cover (in the sense of Enochs) by a small submodule. This answers in the negative a question posed by A.~Amini, B.~Amini, M.~Ershad and H.~Sharif (2007).
Let $M$ be a module. A {\em $δ$-cover} of $M$ is an epimorphism from a module $F$ onto $M$ with a $δ$-small kernel. A $δ$-cover is said to be a {\em flat $δ$-cover} in case $F$ is a flat module. In the present paper, we investigate some properties of (flat) $δ$-covers and flat modules having a projective $δ$-cover. Moreover, we study rings over which every module has a flat $δ$-cover and call them {\em right generalized $δ$-perfect} rings. We also give some characterizations of $δ$-semiperfect and $δ$-perfect rings in terms of locally (finitely, quasi-, direct-) projective $δ$-covers and flat $δ$-covers.