In the presence of radiation absorption, we analyzed the effects of Hall and ion slip effects on an unsteady laminar magnetohydrodynamics convective rotating flow of heat‐producing or absorbing second‐grade fluid across an inclined moving permeable surface in the presence of chemical reaction and radiation absorption. Using the perturbation method, the nondimensional equations for the governing flow are solved to the most excellent conceivable investigative answer. The effects of various factors on velocity, temperature, and concentration are visually and explored in depth. Shear stresses, Nusselt number, and Sherwood number are calculated analytically, rendered computationally in a tabular style, and discussed concerning the essential characteristics for engineering inquiry. It is inferred that an increase in radiation absorption, Hall, and ion slip parameters across the fluid area leads to a rise in the resulting velocity. The thermal and solutal buoyancy forces contribute to the resultant velocity, constantly growing to a very high level. The rotation parameter is used to reduce skin friction, while the Hall and ion slip effects enhance it. The rate of mass transfer increases when the chemical reaction parameter is raised.
The strucure of the set of all non-nilpotent (-1,1) metabelian ring is studied. An additive basis of a free (-1,1) metabelian rings is constructed. It is proved that any identity in a non-nilpotent 2, 3-torsion free (-1,1) metabelian ring of degree greater than or equal to 6 is consequence of four defining identity of M where M is the metabelian (-1,1) ring.Key Words: Non-nilpotent, variety of (-1,1) rings, free metabelian rings, (-1,1) rings. The first example of solvable but not nilpotent alternative and (-1, 1) rings were constructed by Dorofeev [4], [5]. He also gave an example of a finite dimensional right alternative right nilpotent algebra which is not nilpotent. Varieties of two-step solvable nearly associative algebras were studied by many authors [2,6,7,8,9]. Thus Medvedev [9] proved that the varieties of metabelian alternative, Jordan Mal'tsev and type (-1, 1) algebras are specht. Pchelintsev [6] obtained a series results on the structure of lattices of varieties of nearly associative metabelian algebras. In this paper, we study (-1, 1) metabelian rings. They are contained in the class of algebras of type (γ, δ). In this class of ring the square of an ideal is also an ideal and hence called 2-variety. A 2, 3-torsion free ring of type (γ, δ) if satisfies the identities (x, x, x) = 0, * The project is partially supported by University Grants Commission Grants No. 42-17/2013(SR) 2000 Mathematics Subject Classification: 17A30 115Typeset by B S P M style. c Soc. Paran. de Mat. 116K. Jayalakshmi and K. Hari Babu (x, y, z) + γ(y, z, x) + δ(z, y, x) = 0, (x, y, z) − γ(x, z, y) + (1 − δ)(y, z, x) = 0, where γ 2 − δ 2 + δ − 1 = 0, and (x, y, z) = (xy)z − x(yz) is the associator of elements x, y and z. This paper includes the five sections. In sec 2 we prove that the simplest consequences of the defining relations. In sec 3 and 4, operator of the length 3 and 4 are processed. In sec 5 the function {x, y, z} = (yx)z + (zx)y is introduced, its properties are studied, and auxiliary identities necessary for constructing additive bases in free rings are proved. In sec 6, a basis of a free (-1, 1) metabelian rings is constructed and the following main results is proved.
In 1981, Pchelintsev developed the idea for arranging non-nilpotent subvarieties in a given variety by using topological rank for spechtian varieties of algebra as a fixed tool. In this paper we show that for a given topological rank over a field of 2, 3 ? torsion free of (-1; 1) metabelian algebra solvable of index 2 that are Lie-nilpotent of step not more than p is equal to P.
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