Leibnitz-derivation of 0 torsion finite dimensional flexible algebras over an algebraically close... more Leibnitz-derivation of 0 torsion finite dimensional flexible algebras over an algebraically closed field is described. This class of algebra with unit element 1 is nilpotent if and only if it admits an invertible Leibnitz-derivation. This is an analogue to Moens theorem. The proofs are elementary in nature and based on the techniques adopted by Myung and Elduque. AMS Subject Classification: 17A20, 17A32, 17A36.
International Journal of Research -GRANTHAALAYAH, 2015
Some properties of the right nucleus in generalized right alternative rings have been presented i... more Some properties of the right nucleus in generalized right alternative rings have been presented in this paper. In a generalized right alternative ring R which is finitely generated or free of locally nilpotent ideals, the right nucleus Nr equals the center C. Also, if R is prime and Nr ¹ C, then the associator ideal of R is locally nilpotent. Seong Nam [5] studied the properties of the right nucleus in right alternative algebra. He showed that if R is a prime right alternative algebra of char. ≠ 2 and Right nucleus Nr is not equal to the center C, then the associator ideal of R is locally nilpotent. But the problem arises when it come with the study of generalized right alternative ring as the ring dose not absorb the right alternative identity. In this paper we consider our ring to be generalized right alternative ring and try to prove the results of Seong Nam [5]. At the end of this paper we give an example to show that the generalized right alternative ring is not right alternative.
Journal of Ultra Scientist of Physical Sciences Section A, 2018
In this study, we examine the combined effects of thermal radiation, chemical reaction on MHD hyd... more In this study, we examine the combined effects of thermal radiation, chemical reaction on MHD hydromagnetic boundary layer flow over a vertical cone filled with nanofluid saturated porous medium under variable properties. The governing flow, heat and mass transfer equations are transformed into ordinary differential equations using similarity variables and are solved numerically by a Galerkin Finite element method. Numerical results are obtained for dimensionless velocity, temperature, nanoparticle volume fraction, as well as the skin friction, local Nusselt and S herwood number for the different values of the pertinent parameters entered into the problem. The effects of various controlling parameters on these quantities are investigated. Pertinent results are presented graphically and discussed quantitatively. The present results are compared with existing results and found to be good agreement. It is found that the temperature of the fluid remarkably enhances with the rising values of Brownian motion parameter (Nb).
International Journal of Algebra and Statistics, 2014
In this paper, we prove the Common-Denominator property. If \(Q\) is Weak Fountain-Golden Left or... more In this paper, we prove the Common-Denominator property. If \(Q\) is Weak Fountain-Golden Left order in an assosymmetric ring \(R\), then given \(b_{1}\),..., \(b_{n} \in R\) there exist \(a\in S\), \(q_{1}\),..., \(q_{n}\in Q\) such that for every \(i = 1,...,n\), \(b_{i} = \tilde{a} q_{i}0\) and \(a \tilde{a} q_{i}=q_{i}\) and also it is shown that if \(Q\) is subring of an assosymmetric ring \(R\), (i) if $R$ is a weak Fountain-Gould left quotient ring of \(Q\), then \(R\) is a left quotient ring of \(Q\), (ii) suppose $R$ nondegenerate and coinciding with its socle, if \(Q\) is a weak Fountain-Gould left order in \(R\) then \(Q\) is a Fountain-Gould left order in \(R\), (iii) if \(R\) is also artinian then \(Q\) is a classical left order in \(R\) if and only if \(Q\) is a Fountain-Gould left order in \(R\).
Let [Formula: see text] be a 2, 3-torsion-free prime [Formula: see text] ring with commutative ce... more Let [Formula: see text] be a 2, 3-torsion-free prime [Formula: see text] ring with commutative center [Formula: see text]. If [Formula: see text] is not contained in the nucleus [Formula: see text], then a ring defined by a new product [Formula: see text] is nilpotent of index at most 11.
Let R be a non associative ring having Jordan triple Skew derivarion d with an additive subgroup ... more Let R be a non associative ring having Jordan triple Skew derivarion d with an additive subgroup W of R. Such that W + WR = W + RW. If is shown that if W is contained in any two of the three nuclei then the ideal of R generated by W is nilpotent if and only if the subring generated by W is nilpotent.
Journal of Applied Mechanics and Technical Physics, 2012
The group theoretic method is applied for solving the problem of the combined influence of the th... more The group theoretic method is applied for solving the problem of the combined influence of the thermal diffusion and diffusion thermoeffect on magnetohydrodynamic free convective heat and mass transfer over a porous stretching surface in the presence of thermophoresis particle deposition with variable stream conditions. The application of one-parameter groups reduces the number of independent variables by one; consequently, the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. The equations along with the boundary conditions are solved numerically by using the Runge-Kutta-Gill integration scheme with the shooting technique. The impact of the Soret and Dufour effects in the presence of thermophoresis particle deposition with a chemical reaction plays an important role on the flow field.
International Journal of Engineering & Technology, 2018
A ring of type 12(خ³,خ´)"> , was introduced by Albert and Kokoris [1,3] where in they ha... more A ring of type 12(خ³,خ´)"> , was introduced by Albert and Kokoris [1,3] where in they have shown that a simple ring of 12(خ³,خ´)"> type is either associative or contains no idempotent other than 1. In this paper we obtain further results on the residual cases, to prove that a nonassociative (-1,1) rings satisfying (x, x, y)2 = 0, for all elements of the rings imply (x, x, y) = 0. But then indeed (-1,1) rings which have no nilpotent elements are associative and there by all such rings are division rings.
Mathematical Journal of Interdisciplinary Sciences, 2015
In this paper we show how to reduce the study of nondegenerate local Goldie (-1, 1) rings to the ... more In this paper we show how to reduce the study of nondegenerate local Goldie (-1, 1) rings to the strongly prime case, via the notions of uniform ideals and essential subdirect product. also we construct the maximal left quotient ring of (-1, 1) ring that is a left quotient ring of itself. We follow Utumi where a maximal left quotient ring is constructed as a direct limit of partially defined homomorphism from left ideal of R to R.
Boletim da Sociedade Paranaense de Matemática, 2016
The structure of the set of all non- nilpotent (–1, 1) metabelian rings is studied. An additive b... more The structure of the set of all non- nilpotent (–1, 1) metabelian rings is studied. An additive basis of a free (–1, 1) metabelian ring 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 a consequence four defining identities of m where m is the metabelian (–1, 1) ring.
A nonassociative ring which contains a well-known associative ring or left symmetric ring also kn... more A nonassociative ring which contains a well-known associative ring or left symmetric ring also known as Vinberg ring is of great interest. A method to construct Vinberg nonassociative ring is given; Vinberg nonassociative ring is shown as simple; all the derivations of nonassociative simple Vinberg algebra defined are determined; and finally in solid algebra it is shown that if is a nonzero endomorphism of , then is an epimorphism.
Let N be a 2-torsion free s-prime near-ring and 1, a Î Aut N. Let d be a nonzero (1, a)-derivatio... more Let N be a 2-torsion free s-prime near-ring and 1, a Î Aut N. Let d be a nonzero (1, a)-derivation which commutes with s, and L be a nonzeros-Lie ideal, then N is commutative if any one of the following conditions hold. (i) [d(u), u] 1,a = 0. (ii) d(u)u = a(u)d(u) (iii) d(u 2) = ± a(u 2) (iv) d(u 2) = 2 d(u)a(u), for all u Î L.
In this paper we characterize a 2, 3-torsion free nonassociative Vinberg (-1, 1) ring R satisfyin... more In this paper we characterize a 2, 3-torsion free nonassociative Vinberg (-1, 1) ring R satisfying third power associative conditions. In such ring the square of an alternator ideal is trivial, if the ring is nil of index n that does not have elements of order atmost n then the ring is solvable of index atmost n(n+1) 2 + 1 and is locally nilpotent. AMS Subject Classification: 17D20, 17A30 and 17A36.
We give a description on the properties of semideriva-tions in prime rings satisfying certain ide... more We give a description on the properties of semideriva-tions in prime rings satisfying certain identities. Some well known results characterizing commutativity of prime rings by derivations have been generalized using semiderivations.
Leibnitz-derivation of 0-torsion finite dimensional flexible algebras over an algebraically close... more Leibnitz-derivation of 0-torsion finite dimensional flexible algebras over an algebraically closed field is described. This class of algebra with unit element 1 is nilpotent if and only if it admits an invertible Leibnitz-derivation. This is an analogue to Moens theorem. The proofs are elementary in nature and based on the techniques adopted by Myung and Elduque.
Background: First examples of simple nonassociative superalgebras were constructed by Shestakov i... more Background: First examples of simple nonassociative superalgebras were constructed by Shestakov in (1991 and 1992). Since then many authors showed interest towards the study of superalgebras and superalgebras of vector type. Materials and Methods: Multiplication in M is uniquely defined by a fixed finite set of derivations and by elements of A. The types of derivations used in this article to obtain the results are the near derivation , the derivation and the derivation Results: The flexible Lie - admissible superalgebra over a 2, 3 – torsion free field on one odd generator e is isomorphic to the twisted superalgebra with the free generator In a 2, 3 – torsion free flexible Lie - admissible superalgebras of vector type F, the even part A is differentiably simple, associative and commutative algebra and the odd part M is a finitely generated associative and commutative A – bimodule. Conclusions: A connection between the integral domains, the finitely generated projective modules over them, the derivations of an integral domain and the flexible Lie – admissible superalgebras of vector type has been established. Main conclusions: If A is an integral domain and be a finitely generated projective A-module of rank 1, then is a flexible Lie - admissible superalgebra with even part A and odd part M provided that the mapping is a nonzero derivation of A into the A - module , is a set of derivations of A where .
In this paper we have obtained solutions of Riemann-Liouville fractional matrix differential equa... more In this paper we have obtained solutions of Riemann-Liouville fractional matrix differential equation (RLFMDE) of the form D q X = AX and D q X = AX + XB. We have extended these results to 2 nd order and 3 rd order RLFMDE and then generalized them to n th order RLFMDE.
abstract: The strucure of the set of all non-nilpotent (-1,1) metabelian ring is
studied. An addi... more abstract: 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.
Uploads
Papers by Jaya Lakshmi
Materials and Methods: Multiplication in M is uniquely defined by a fixed finite set of derivations and by elements of A. The types of derivations used in this article to obtain the results are the near derivation , the derivation and the derivation
Results: The flexible Lie - admissible superalgebra over a 2, 3 – torsion free field on one odd generator e is isomorphic to the twisted superalgebra with the free generator In a 2, 3 – torsion free flexible Lie - admissible superalgebras of vector type F, the even part A is differentiably simple, associative and commutative algebra and the odd part M is a finitely generated associative and commutative A – bimodule.
Conclusions: A connection between the integral domains, the finitely generated projective modules over them, the derivations of an integral domain and the flexible Lie – admissible superalgebras of vector type has been established.
Main conclusions: If A is an integral domain and be a finitely generated projective A-module of rank 1, then is a flexible Lie - admissible superalgebra with even part A and odd part M provided that the mapping is a nonzero derivation of A into the A - module , is a set of derivations of A where .
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.