We define and examine in-depth the notion of a weakly reversible ring showing that all weakly reversible rings are abelian McCoy rings and so, in particular, they are abelian 2-primal rings. Moreover, we construct a weakly reversible ring which is not reversible. We also prove that, if R is a weakly reversible ring, then the polynomial ring R[x] is strongly AB. Thus, in particular, the weakly reversible ring R is zip if, and only if, R[x] is zip. We, moreover, establish that if R is a weakly reversible ring and every prime ideal of R is maximal, then both R and R[x] are AB rings.
The main focus of this study is the investigation of a time fractional higher-order Broer-Kaup (BK) system which, to the best of our knowledge, has not been reported previously in terms of Riemann-Liouville (RL) and Caputo fractional derivatives. Performing the similarity reduction formalism, the time fractional higher-order BK system is reduced into a system of fractional nonlinear ODEs. Moreover, the power series solutions are derived, including their convergence analysis. By considering the obtained symmetries, conserved quantities of the system under consideration are formulated based on the nonlinear self-adjointness property for fractional differential equations, and the nontriviality property is also checked. In view of the Sumudu-Adomian decomposition method, we obtain a set of analytical solutions. To show the effectiveness of this employed method, we analyze the influence of the fractional order and explore the dynamic behavior of the constructed solutions through graphical representations.
Let (X,d,μ ) be an RD-space satisfying the doubling condition in the sense of Coifman and Weiss and a certain reverse doubling condition. In this setting, the authors first investigate a weighted John–Nirenberg inequality for the space BMO_θ ,φ(X) introduced in Lu, G.; Wang, M.: Characterizations of spaces BMO_θ ,φ(X) on RD-spaces., which extends some known results on BMO -type spaces on Euclidean spaces and RD-spaces. Furthermore, some useful characterizations of spaces BMO_θ ,φ(X) are established.
In this research paper, we study various central differential identities on prime rings with anti-automorphism involving generalized derivations. The forms of these maps satisfying some special identities are examined utilizing the theory of functional identities.
