Jordan Journal of Mathematics and Statistics

On some Factor Rings and their Connections with Derivations

Lahcen Oukhtite, Abdellah Mamouni, Mohammed Zerra — Thu, 20 Mar 2025 00:00:00 +0300

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.

Key words and phrases. Prime ideal, factor ring, commutativity, derivations.

2020 Mathematics Subject Classification. 16N60, 16U80

Multiplication Γ-Semigroups

J. A. Awolola, M. A. Ibrahim — Thu, 20 Mar 2025 00:00:00 +0300

In this paper, we define the concept of non-commutative right multiplication Γ-semigroup as a generalization of non-commutative right multiplication semigroups using right Γ-ideals. We prove some results related to regular Γ-semigroups, simple Γ-semigroups, semisimple Γ-semigroups and cancellative Γ-semigroups.

Key words and phrases. Γ-semigroup, multiplication Γ-semigroup.

2000 Mathematics Subject Classification. 18B99, 20M99

Difference Cesaro Sequence Space Defined by Musielak-Orlicz Functions

Vivek Kumar, Sunil K. Sharma, Ajay K. Sharma — Thu, 20 Mar 2025 00:00:00 +0300

The main goal of this paper is to study the topological and algebraic properties of the new constructed Ces`aro sequence space of difference operator by means of Musielak-Orlicz functions. We also make an effort to study the properties of composite of Museilak-Orlicz function.

Key words and phrases. Ces`aro sequence space, difference operator, Modulus function.

2020 Mathematics Subject Classification. 46A45, 40A05, 40C05

On Pseudo-Balancing of Path-Induced Signed Graphs

Jomon Kottarathil — Thu, 20 Mar 2025 00:00:00 +0300

The path decomposition of a graph G is the partition of its edges into distinct paths. Pendant number of a graph G is the least number of terminal vertices involved in the path decomposition of G. If the signed function is induced by the terminal vertices of the path-decomposed graph, it is called path-induced signed graph. In this paper, we identify few classes of balanced signed graphs and also introduce and examine a related concept, namely, pseudo-balancing of path-induced signed graphs.

Key words and phrases. Path decomposition, pendant number, signed graphs, path-induced signed graphs, pseudo-balanced path-induced signed graphs.

2010 Mathematics Subject Classification. MSC 05C22; 05C38

On a Class of Degenerate Fractional p(.)-Laplacian Problems with Variable order and Variable Exponent

Abdelali Sabri — Thu, 20 Mar 2025 00:00:00 +0300

Theaimofthis paper isto study a class of a degenerate elliptic problem driven by the fractional p(.)-Laplacian operator with variable order and variable exponent, the main tool used here is the variational method combined with the theory of variable-order fractional Sobolev spaces with variable exponent.

Key words and phrases. Existence, fractional p(x)-Laplacian, fractional Sobolev space, uniqueness, variable exponent, variable order, weak solution.

2010 Mathematics Subject Classification. 34A08, 35A15, 46E35, 35R11, 35S15

On Holomorph of WIP PACC Loops

Olufemi. O. George — Thu, 20 Mar 2025 00:00:00 +0300

This workinvestigates the holomorph of a weak inverse property power associative conjugacy closed (WIP PACC) loop. It is shown that the holomorph of a WIP PACC loop is WIP PACC. If Q is a WIP PACC loop and A is the automorphism group of Q, then each θ ∈ A is a nuclear automorphism. The A(Q) holomorph of a WIP PACC loop is shown to satisfy the doubly weak inverse property. A necessary and sufficient condition for the holomorph of an arbitrary loop and its automorphism group to produce a WIP PACC loop is established.
Finally, if Q is a LWPC (RWPC) loop with x ∈ Nµ(Q), then the holomorph of Q is an extra loop.

Key words and phrases. left (right) conjugacy closed loop, power associative, weak inverse property, LWPC-loop, RWPC-loop, WIP PACC loop, holomorph.

2010 Mathematics Subject Classification. 20N02, 20N05

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

S. Djenaoui, B. Meftah — Thu, 20 Mar 2025 00:00:00 +0300

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.

Key words and phrases. Maclaurin’s formulae, Newton-Cotes quadrature, s-convex functions.

2010 Mathematics Subject Classification. 26D10, 26D15, 26A51

On Weakly K-Clean Rings

Fatemeh Rashedi — Thu, 20 Mar 2025 00:00:00 +0300

In this paper, we offer a new generalization of the k-clean ring that is called weakly k-clean ring. Let 2 ≤ k ∈ N. Then the ring R is said to be a weakly k-clean if for each a ∈ R there exist u ∈ U(R) and e ∈ 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.

Key words and phrases. weakly k-clean ring, k-clean ring.

2010 Mathematics Subject Classification. 16U99, 16Z05

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

Mohamed Bourza — Thu, 20 Mar 2025 00:00:00 +0300

Weconsiderthe Euler-Maruyamaapproximationfor 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 dX_t = σ(t,X_t)dB_t + 1/2σ(t,X_t)σ′_x(t,X_t)dt + β(t)dL⁰_t(X). After that we use a transformation technique that removes the discontinuity from the drift of the new auxiliary equation without local time, such that the coefficients of the obtained time-inhomogeneous SDE are Lipschitz continuous in space. Thus the Euler-Maruyama method can be applied and we provide the rate of strong convergence desired.

Key words and phrases. stochastic differential equations, local time, Euler-Maruyama method, discontinuous coefficients.

2010 Mathematics Subject Classification. 60H35, 60H10, 60J55, 65C30

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

A. K. Alomari, Rula Shraideh — Thu, 20 Mar 2025 00:00:00 +0300

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.

Key words and phrases. analytic solution , homotopy analysis method, fractional Allen-Cahn equation, fractional calculus.

2010 Mathematics Subject Classification. 65D15, 26A33, 35R11

The Dual of the Notions n-Submodules and J-Submodules

Faranak Farshadifar — Thu, 20 Mar 2025 00:00:00 +0300

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

Key words and phrases. n-submodule, J-submodule, co-n-submodule, and co-J-submodule.

2010 Mathematics Subject Classification. 13C13, 13C99

Fractional Simpson Like Type Inequalities for Differentiable s-Convex Functions

S. Bouhadjar, B. Meftah — Thu, 20 Mar 2025 00:00:00 +0300

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.

Key words and phrases. 3/8-Simpson inequality, Riemann-Liouville integral operators, s-convex functions, H¨older inequality.

2010 Mathematics Subject Classification. 26D10, 26D15, 26A51

Amalgamations of Potent, Semipotent, and Semisuitable Rings

Khalid Adarbeh, Mohammad Adarbeh — Thu, 20 Mar 2025 00:00:00 +0300

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.

Key words and phrases. Amalgamation of a ring along an ideal, trivial ring extension, suitable rings, semi-suitable rings, potent rings, semi potent rings.

2010 Mathematics Subject Classification. Primary 13C10, 13C11, 13E05, 13F05, 13H10; Secondary 16A30,16A50,16A52