A generalization of quantales with applications to modules and rings

Bárcenas, Mauricio Medina; Zaldívar-Corichi, Luis Ángel; Sandoval-Miranda, Martha Lizbeth Shaid

doi:10.1016/j.jpaa.2015.10.004

Cited by 5 publications

(3 citation statements)

References 12 publications

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“…Note that when R = M , Spec(M ) is the usual prime spectrum. As it was noticed in [MBSMZC16,Example 4…”

Section: Remark 28 ([Mbsmzc16]supporting

confidence: 66%

“…Following this way, in Section 5, we study properties of (N : L) for fully invariant submodules of a module M, we study the strong algebraic De Morgan's law, and finally, in Theorem 5.16 is given a characterization for a Noetherian prime ring to be an Asano prime ring. By last, it is worth to mention that this manuscript is a natural step in our investigation, that was initiated in [MBSMZC16] followed by [MBMCSMZC18] and [MBMCSMZC20].…”

Section: Introductionmentioning

confidence: 99%

“…[MBSMZC16].Definition 2.4. A (quasi)quantale A is a complete lattice with an associative product A × A → A such that for all (directed) subsets X, Y ⊆ A and a ∈ A :(X) a = {xa | x ∈ X} and a ( Y ) = {ay | y ∈ Y }.Definition 2.5.…”

mentioning

confidence: 99%

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On the De Morgan’s Laws for Modules

Bárcenas

Sandoval-Miranda

Zaldívar-Corichi

2021

Appl Categor Struct

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In this investigation we give a module-theoretic counterpart of the well known De Morgan's laws for rings and topological spaces. We observe that the module-theoretic De Morgan's laws are related with semiprime modules and modules in which the annihilator of any fully invariant submodule is a direct summand. Also, we give a general treatment of De Morgan's laws for ordered structures (idiomatic-quantales). At the end, the manuscript goes back to the ring theoretic realm, in this case we study the non-commutative counterpart of Dedekind domains, and we describe Asano prime rings using the strong De Morgan law.

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“…Note that when R = M , Spec(M ) is the usual prime spectrum. As it was noticed in [MBSMZC16,Example 4…”

Section: Remark 28 ([Mbsmzc16]supporting

confidence: 66%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the De Morgan’s Laws for Modules

Bárcenas

Sandoval-Miranda

Zaldívar-Corichi

2021

Appl Categor Struct

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Attaching topological spaces to a module (I): Sobriety and spatiality

Bárcenas

Morales-Callejas

Sandoval-Miranda

et al. 2018

Journal of Pure and Applied Algebra

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On the structure of Goldie modules

Pérez

Bárcenas

Montes

et al. 2017

Communications in Algebra

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Given a semiprime Goldie module M projective in σ[M ] we study decompositions on its M -injective hull M in terms of the minimal prime in M submodules. With this, we characterize the semiprime Goldie modules in Z-Mod and make a decomposition of the endomorphism ring of M . Also, we investigate the relations among semiprime Goldie modules, QI-modules and co-semisimple modules extending results on left QI-rings and V -rings.

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A generalization of quantales with applications to modules and rings

Cited by 5 publications

References 12 publications

On the De Morgan’s Laws for Modules

On the De Morgan’s Laws for Modules

Attaching topological spaces to a module (I): Sobriety and spatiality

On the structure of Goldie modules

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