Let M be a torsion-free module over an integral domain D with its quotient field K. In 2022,
Nurwigantara et al. introduced the concept of a completely integrally closed module (CICM …

Let R=⊕ n∈ ℤ R n be a strongly graded ring of type ℤ such that R 0 is a prime Goldie ring
with its quotient ring Q 0. It is shown that the following three conditions are equivalent:(i) R 0 …

Let $ M=\oplus_ {n\in\mathbb {Z}} M_ {n} $ be a strongly graded module over strongly
graded ring $ D=\oplus_ {n\in\mathbb {Z}} D_ {n} $. In this paper, we prove that if $ M_ {0} …

Let $ R=\oplus_ {n\in\Z} R_ {n} $ be a strongly graded ring of type $\Z $ and $ R_ {0} $ is a
prime Goldie ring. It is shown that the following three conditions are equivalent:(i) $ R_ {0} …