Right-Left Symmetry of Right Nonsingular Right Max-Min CS Prime Rings

Max CS and min CS modules

“…Section 3 studies symmetry of max-min CS property and uniform dimension on the endomorphism rings of max-min CS modules. There, we generalize the results of Jain et al in [2].…”

“…Jain et al [2] studied the right-left symmetry of max-min CS condition on prime rings. In this section, we aim to generalize such the results to prime modules.…”

“…For a submodule X of M, we write We adopt the notions of primeness and semiprimeness in module category introduced by Sanh et al in [7]. Recall that a min CS module ( [2] and [8].…”

On CS- Rings

“…Following [4], a ring R is said to be right (left) CS-ring if every nonzero right (left) ideal is essential in a direct summand, equivalently, every right (left) closed ideal is a direct summand [6]. It can be checked that R is CS-ring.…”

“…ex=exe), for all xR [1]. A right ideal I of a ring R is closed if there is no right ideal of R which is a proper essential extension of I [6], clearly every maximal right ideal is right closed.…”