Quasi J-ideals of Commutative Rings

Let $R$ be a commutative ring with identity. In this paper, we introduce the concept of quasi $J$-ideal which is a generalization of $J$-ideal. A proper ideal of $R$ is called a quasi $J$-ideal if its radical is a $J$-ideal. Many characterizations of quasi $J$-ideals in some special rings are obtained. We characterize rings in which every proper ideal is quasi $J$-ideal. Further, as a generalization of presimplifiable rings, we define the notion of quasi presimplifiable rings. We call a ring $R$ a quasi presimplifiable ring if whenever $a,b\in R$ and $a=ab$, then either $a$ is a nilpotent or $b$ is a unit. It is shown that a proper ideal $I$ that is contained in the Jacobson radical is a quasi $J$-ideal (resp. $J$-ideal) if and only if $R/I$ is a quasi presimplifiable (resp. presimplifiable) ring

Semi n-ideals of commutative rings

Let R be a commutative ring with identity. A proper ideal I is said to be an n-ideal of R if for a, b ∈ R, ab ∈ I and a∉0 imply b ∈ I. We give a new generalization of the concept of n-ideals by defining a proper ideal I of R to be a semi n-ideal if whenever a ∈ R is such that a2 ∈ I, then a∈0 or a ∈ I. We give some examples of semi n-ideal and investigate semi n-ideals under various contexts of constructions such as direct products, homomorphic images and localizations. We present various characterizations of this new class of ideals. Moreover, we prove that every proper ideal of a zero dimensional general ZPI-ring R is a semi n-ideal if and only if R is a UN-ring or R ≌ F1 × F2 × … × Fk, where Fi is a field for i = 1,…, k. Finally, for a ring homomorphism f: R → S and an ideal J of S, we study some forms of a semi n-ideal of the amalgamation R ⋈fJ of R with S along J with respect to f. © 2022, Institute of Mathematics, Czech Academy of Sciences

ON WEAKLY S-PRIME SUBMODULES

Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N:R M)∩S = ∅ to be weakly S-prime if there exists s ∈ S such that whenever a ∈ R and m ∈ M with 0 ≠ am ∈ N, then either sa ∈ (N:R M) or sm ∈ N. Many properties, examples and characterizations of weakly S-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly S-prime. © 2022 Korean Mathematical Society

Weakly J-ideals of Commutative Rings

Let $R$ be a commutative ring with non-zero identity. In this paper, we introduce the concept of weakly $J$-ideals as a new generalization of $J$-ideals. We call a proper ideal $I$ of a ring $R$ a weakly $J$-ideal if whenever $a,b\in R$ with $0\neq ab\in I$ and $a\notin J(R)$, then $a\in I$. Many of the basic properties and characterizations of this concept are studied. We investigate weakly $J$-ideals under various contexts of constructions such as direct products, localizations, homomorphic images. Moreover, a number of examples and results on weakly $J$-ideals are discussed. Finally, the third section is devoted to the characterizations of these constructions in an amagamated ring along an ideal

Semi r-ideals of commutative rings

For commutative rings with identity, we introduce and study the concept of semi r-ideals which is a kind of generalization of both r-ideals and semiprime ideals. A proper ideal I of a commutative ring R is called semi r-ideal if whenever a (2)?I and Ann (R)(a) = 0, then a ? I. Several properties and characterizations of this class of ideals are determined. In particular, we investigate semi r-ideal under various contexts of constructions such as direct products, localizations, homomorphic images, idealizations and amalagamations rings. We extend semi r-ideals of rings to semi r-submodules of modules and clarify some of their properties. Moreover, we define submodules satisfying the D-annihilator condition and justify when they are semi r-submodules

The Impact of COVID-19 on the Relationship between Non-Renewable Energy and Saudi Stock Market Sectors Using Wavelet Coherence Approach and Neural Networks

In this study, we examine the impact of COVID-19 on the relationship between non-renewable energy and Saudi stock market sectors for the period 11 January 2017–22 January 2022. We apply wavelet coherence and Radial Basis Function Neural Network (RBFNN) models. Our results provide evidence that COVID-19 led to an increase in the strength of the relationship between oil as a main non-renewable energy source and Saudi stock market sectors and affected the nature and direction of this relationship. The relationships between oil and commercial and professional services, materials, banks, energy, and transportation sectors are the most affected. Our results will help hedge funds, mutual funds, and individual investors, forecast the direction of Saudi stock market sectors and the use of oil for hedging or diversification during periods of uncertainty and crisis. It will also help decision and policymakers in Saudi Arabia to make the necessary decisions and actions to maintain the stability of the stock market sectors during these periods.Deanship of Scientific Research at the Imam Abdulrahman bin Faisal University, Saudi Arabia, grant number 2019-155-ASCS