2018
Том 70
№ 12

# On principal ideal multiplication modules

Abstract

Let $R$ be a commutative ring with identity and let $M$ be a unitary $R$-module. A submodule $N$ of $M$ is said to be a multiple of $M$ if $N = rM$ for some $r \in R$. If every submodule of $M$ is a multiple of $M$, then $M$ is said to be a principal ideal multiplication module. We characterize principal ideal multiplication modules and generalize some results from [Azizi A. Principal ideal multiplication modules // Algebra Colloq. – 2008. – 15. – P. 637 – 648].

Citation Example: Azizi A., Jayaram C. On principal ideal multiplication modules // Ukr. Mat. Zh. - 2017. - 69, № 3. - pp. 291-299.