Let R be a ring with identity and M be a unitary left R-module. The complement of the
intersection graph of submodules of M, denoted by Γ (M), is defined to be a graph whose …

Let R be a ring with identity and M be a unitary left R-module. The intersection graph of
submodules of M, denoted by G (M), is defined to be a graph whose vertices are in one to …

In this article, a new radical formula for a module over a commutative ring is introduced by
constructing a generalization of radical and envelope and defining an (e, r)-radical formula …

A bounded partially ordered set (P, 0, 1,≤) is lower finite provided P is infinite and for each
x≠ 1 in P, there are but finitely many elements y in P such that y< x. We will call a module M …

Given a cyclic group $ G $ of order $ p^ r $, where $ p $ is a prime and $ r\in\mathbb {N} $. It
is well-known that the order of its greatest proper subgroup $\psi (G) $ and the number of its …