Let R be a commutative ring and M be an R-module. A submodule N of M is called a d-
submodule ( resp., an fd-submodule ) if \ann_R(m)⊆\ann_R(m') ( resp …

In this paper we prove that each element of any regular Baer ring is a sum of two units if no
factor ring of $ R $ is isomorphic to $ Z_2 $ and we characterize regular Baer rings with unit …

In this paper, we investigate various kinds of extensions of twin-good rings. Moreover, we
prove that every element of an abelian neat ring R is twin-good if and only if R has no factor …

In this paper, we prove that every element in an exchange ring $ R $ with artinian primitive
factors is $ n $-tuplet-good iff $1 _R $ is $ n $-tuplet-good. Also, we show that for such rings …

In this thesis, we characterize semisimple modules over noncommutative rings and
investigate their properties. We discuss noncommutative rings and their modules based on …