On some Factor Rings and their Connections with Derivations

Our purpose in this paper is to investigate certain central valued identities on a factor ring with respect to a prime ideal P of a ring R, involving a pair of derivations of R. Some well-known results characterizing commutativity of prime (semi-prime) rings have been generalized.

Vivek Kumar
Sunil K. Sharma
Ajay K. Sharma


 

JJMS, 2023, 16(3), 421-430

Jomon Kottarathil




 

Abdelali Sabri



 

JJMS, 2023, 16(3), 445-462

Olufemi. O. George




 

JJMS, 2023, 16(3), 463-482

Fractional Maclaurin Type Inequalities for Functions whose First Derivatives are s-Convex Functions

Classical and fractional integral inequalities have become a popular method and a powerful tool for estimating errors of quadrature formulas. Several studies on various types of inequality have been conducted and the literature in this area is vast and diverse. The current study intends to investigate one of the open three-point Newton-Cotes formulae, known as Maclaurin’s formula, using Riemann-Liouville fractional operators. To accomplish so, we first created a new identity.
From this identity and through the s-convexity, we have established some new Maclaurin-type inequalities, we also discussed the cases that can be derived of our finding. Furthermore, various applications for error estimates are offered to demonstrate the efficacy of our primary results.

S. Djenaoui
B. Meftah


 

JJMS, 2023, 16(3), 483-506

On Weakly K-Clean Rings

In this paper, we offer a new generalization of the k-clean ring that is called weakly k-clean ring. Let 2 ≤ k ϵ N. Then the ring R is said to be a weakly k-clean if for each a ϵ R there exist u ϵ U(R) and e ϵ Pk(R) such that a = u+e or a = u−e. We obtain some properties of weakly k-clean rings. It is shown that each homomorphic image of a weakly k-clean ring is weakly k-clean. Also, it is proved that the ring R[R, S] is weakly k-clean if and only if R is k-clean and S is weakly k-clean.

Fatemeh Rashedi



 

JJMS, 2023, 16(3), 507-513

Euler-Maruyama Approximation for Diffusion Process Generated by Divergence form Operator with Discontinuous Coefficients

We consider the Euler-Maruyama approximation for time-inhomogeneous one-dimensional stochastic differential equations involving the local time (SDELT), generated by divergence form operators with discontinuous coefficients at zero. We use a space transform in order to remove the local time L⁰_t from the stochastic
differential equation of type .......................

Mohamed Bourza


 

JJMS, 2023, 16(3), 515-533

Approximate Solution of Fractional Allen-Cahn Equation by The Mittag-Leffler Type Kernels

This study presents the approximate analytic solution of the fractional Allen-–Cahn equation involving fractional-order derivatives with the Mittag-Leffler type kernels. The fractional derivative contains three parameters that can adjust the model. We utilize the homotopy analysis method (HAM) to generate the solution of the fractional differential equations. The effect of the fractional parameters on the solution behaviors is studied, and the approximate analytical solution of the fractional Allen-–Cahn equation has been acquired successfully. Numerical results are given through graphs and tables. Since the exact solution of the obtained differential equation is unknown, we calculate the residual error to demonstrate the algorithm’s efficiency.

A. K. Alomari
Rula Shraideh



 

JJMS, 2023, 16(3), 535-549

The dual of the notions n-submodules and J-submodules

Let R be a commutative ring with identity and M be an R-module. A proper submodule N of M is called an n-submodule if for a ϵ R, m ϵ M, am ϵ N with ........ , implies m ϵ N. A proper submodule N of M is called a J-submodule of M if for a ϵ R and m ϵ M, whenever am ϵ N and a ∈ (J(R)M : M), then m ϵ N. The aim of this paper is to introduce and investigate the dual notions of n-submodules and J-submodules of M.  

Faranak Farshadifar

JJMS, 2023, 16(3), 551-562

Convexity inequalities are very important for fractional calculus and its efficiency in many applied sciences. This field has become increasingly popular and represents a powerful tool for estimating errors of quadrature formulas. In this paper, we seek to develop new four-point Simpson-type inequalities involving Riemenn-Liouville integral operators. To do this, we first propose a new integral identity. By using this identity we establish some new fractional Simpson like type inequalities for functions whose first derivatives are s-convex in the second sense.
Some particular cases are also discussed. We provid at the end some applications to special means to demonstrate the effectiveness of our results.

JJMS, 2023, 16(3), 563-584

We investigate the transfer of the notion of semisuitable, potent, and semipotent rings in different settings of the amalgamated algebras along an ideal. We put the transfer results in use to provide examples subject to the involved ring theoretic notions as well as to recover some previous results related to the transfer of these notions in other constructions such as trivial ring extension.

JJMS, 2023, 16(3), 585-597