Journal of Mathematical Extension
Volume:16 Issue: 1, Jan 2022

Let R be a commutative ring with identity. We give a new generalization to prime ideals called α-prime ideal. A proper ideal P of R is called an α-prime ideal if for all a, b in R with ab ∈ P, then a ∈ P or α(b) ∈ P where α ∈ End(R). We study some properties of α-prime ideals analogous to prime ideals. We give some characterizations for such generalization and we prove that the intersection of all α-primes in a ring R is the set of all α-nilpotent elements in R. Finally, we give new versions of some famous theorems about prime ideals including α-integral domains and α-fields.

In this paper, we first introduce a class of finite group Gf which is covered all finite metacyclic 2-groups of negative type in Beuelre’s classification. Next, we obtain the size of centralizers and also conjugate type vector of the groups. Finally, the n-th commutativity degree of Gf is obtained as a direct application of the results.

In this paper, we first characterize quasi-multipliers of (M(G) ∗ 0) ∗ and show that the Banach algebra of all quasi-multipliers of (M(G) ∗ 0) ∗ is isometrically isomorphic to (M(G) ∗ 0) ∗ . We also establish that quasi-multipliers of (M(G) ∗ 0) ∗ are separately continuous. Then, we investigate the existence of weakly compact quasi-multipliers of (M(G) ∗ 0) ∗ . Finally, we prove that the Banach algebra of quasimultipliers of (M(G) ∗ 0) ∗ is commutative if and only if G is abelian and discrete.

In this paper, we investigate some qualitative properties of a class of nonlinear singular systems with multiple constant delays. By using the Lyapunov-Krasovskii functional (LKF) method and integral inequalities, we obtain some new sufficient conditions which guarantee that the considered systems are regular, impulse-free and exponentially stable. Two numerical examples are provided to illustrate the application of the obtained results using MATLAB software. By this paper, we extend and improve some results in the literature.

In this paper, we introduce the concept of j-hom-derivation, j ∈ {1, 2} and solve the new generalized additive-quadratic functional equations in the sense of ternary Banach algebras. Moreover, using the fixed point method, we prove its Hyers-Ulam stability.

In this article, we present a stabilized finite element (FE) method for the linearized viscoelastic fluid flow problems by Discontinuous Galerkin (DG) Method. The FE spaces for the unknown variables are chosen as P1−P0−P1, where the fluid velocity and the pressure are discretized by the lowest-order Lagrange elements and the stress tensor is discretized by piecewise P1 polynomial. In order to get a stable scheme, we added a stabilization term in the discretized weak formulation. This method has some prominent features: parameter-free, avoiding calculation of higher-order derivatives and its behaviour towards pressure is totally local. We obtained optimal error estimates and presented several numerical experiments to verify the proposed scheme.