Some Results on Locally Noetherian Modules and Locally Ar- tinian Modules Page 1
KYUNGPOOK Math. J. 58(2018), 1-8 https://doi.org/10.5666/KMJ.2018.58.1.1 pISSN 1225-6951 …

Let (R, 𝔪) be a Noetherian local ring, A an Artinian R-module, and M a finitely generated R-
module. Consider the following property: We say that A is quasi unmixed if for all In this …

Let (R, m) be a complete Noetherian local ring, I an ideal of R and M a nonzero Artinian R-
module. In this paper it is shown that if p is a prime ideal of R such that dim R/p= 1 and (0: M …

For a commutative local ring R, we know that every ideal is a direct sum of local modules if
and only if the unique maximal ideal M of R is of the form M= R x⊕ R y⊕(⊕ γ∈ Γ R s γ) …

A theorem from commutative algebra due to Köthe and Cohen-Kaplansky states that,“a
commutative ring R has the property that every R-module is a direct sum of cyclic modules if …

Let $ R $ be a commutative Noetherian ring. It is shown that $ R $ is Artinian if and only if
every $ R $-module is good, if and only if every $ R $-module is representable. As a result, it …

A well-known result of Köthe and Cohen-Kaplansky states that a commutative ring R has the
property that every R-module is a direct sum of cyclic modules if and only if R is an Artinian …

Let R be a commutative Noetherian ring, I, J two ideals of R, and M an R-module. For a non-
negative integer t, we show:(a) If for all j< t and are finite (resp., Artinian), then is finite (resp …

Matlis showed that the injective hull of a simple module over a commutative Noetherian ring
is Artinian. In several recent papers, non-commutative Noetherian rings whose injective …

A module M satisfies the restricted minimum condition if M/N is artinian for every essential
submodule N of M. A ring R is called a right RM-ring whenever $ R_ {R} $ satisfies the …