In this paper we introduce a lattice structure as a generalization of meet-continuous lattices
and quantales. We develop a point-free approach to these new lattices and apply these …

For an R-module M, projective in σ [M] and satisfying ascending chain condition on left
annihilators, the authors introduce the concept of Goldie module. The authors also use the …

A module M is called a D4-module if, whenever A and B are submodules of M with M= A⊕ B
and f: A→ B is a homomorphism with Imf a direct summand of B, then Kerf is a direct …

We introduce the notions of strongly harmonic and Gelfand module, as a generalization of
the well-known ring theoretic case. We prove some properties of these modules and we …

Using the concept of prime submodule defined by Raggi et al. in, for M∈ R-Mod we define
the concept of classical Krull dimension relative to a hereditary torsion theory τ∈ M-tors. We …

1. Introduction Page 1 TAIWANESE JOURNAL OF MATHEMATICS Vol. 22, No. 3, pp. 545–565,
June 2018 DOI: 10.11650/tjm/171102 Primitive Submodules, Co-semisimple and Regular …

In this paper we study some frames associated to an R-module M. We define semiprimitive
submodules and we prove that they form an spatial frame canonically isomorphic to the …

Using the concepts of prime module, semiprime module and the concept of ascending chain
condition (ACC) on annihilators for an R-module M, we prove that if M is semiprime and …

For a multiplication $ R $-module $ M $ we consider the Zariski topology in the set $
Spec\left (M\right) $ of prime submodules of $ M $. We investigate the relationship between …

In this paper, we introduce the notion of abelian endoregular modules as those modules
whose endomorphism rings are abelian von Neumann regular. We characterize an abelian …