The aim of the present paper is to characterize associative rings R with unity in which 1+eR(1-e) terms some important class literature (for example, NR-rings, UU-rings, UJ-rings, UR-rings, exchange rings, 2-primal rings), where e2=e∈ and U(R) set units R.

The time-dependent acoustic field generated by the mutual interaction of a pair of coaxial viscous vortex rings advecting along a common axis of symmetry is simulated using a two-step numerical procedure. In the first step, the flowfield is predicted by solving the incompressible Navier–Stokes equations. In the second step, Powell’s vortex sound theory is used to predict the far-field acoustic ...

This paper focuses on the set-oriented operations and algebraic structures of soft sets. Relatedly, in this paper, firstly some essential properties $\alpha$-intersection set are investigated, where $\alpha$ is a non-empty subset universal set. Later, by using set, notion set-generated subring ring introduced. The generators intersections products subrings given. Some related about investigated...