We shall prove that if is a finitely generated multiplication module and is a finitely generated ideal of , then there exists a distributive lattice such that with Zariski topology is homeomorphic to to Stone topology. Finally we shall give a characterization of finitely generated multiplication -modules such that is a finitely generated ideal of .
We investigate some properties of -submodules. More precisely, we find a necessary and sufficient condition for every proper submodule of a module to be an -submodule. Also, we show that if is a finitely generated -module and is a prime ideal of , then has -submodule. Moreover, we define the notion of -submodule, which is a generalization of the notion of -submodule. We find some characterizations of -submodules and we examine the way the aforementioned notions are related to each...
We find complete sets of generating relations between the elements [r] = rⁿ - r for and for n = 3. One of these relations is the n-derivation property [rs] = rⁿ[s] + s[r], r,s ∈ R.
First, we give a complete description of the indecomposable prime modules over a Dedekind domain. Second, if is the pullback, in the sense of [9], of two local Dedekind domains then we classify indecomposable prime -modules and establish a connection between the prime modules and the pure-injective modules (also representable modules) over such rings.
We characterize prime submodules of for a principal ideal domain and investigate the primary decomposition of any submodule into primary submodules of
The purpose of this paper is to present a new approach to the classification of indecomposable pseudo-prime multiplication modules over pullback of two local Dedekind domains. We extend the definitions and the results given by Ebrahimi Atani and Farzalipour (2009) to more general cases.