Derivations with invertible values in flexible algebras

Gangireddy Lakshmi Devi; K. Jayalakshmi

doi:10.5269/bspm.v38i6.37192

Gangireddy Lakshmi Devi Jawaharlal Nehru Technological University Ananthapur A.P. India.
K. Jayalakshmi JNTUA College Of Engineering (Anathapuramu) Department of Mathematics

DOI: https://doi.org/10.5269/bspm.v38i6.37192

Resumen

Derivations with invertible values of 0 – torsion flexible algebras satisfying x(yz) = (xz)y over an algebraically closed field are described. For this class of algebra with unit element 1 and derivation with invertible value d is either a Cayley – Dickson algebra over its center Z(A) or a factor algebra of polynomial algebra C[a]/(a2) over a Cayley – Dickson division algebra; also C is 2 – torsion, d(C) = 0 and d(a) = 1+ua for some u in center of C and d is an outer derivation. Moreover, C is a split Cayley – Dickson algebra over its center Z having a derivation with invertible value d if and only if C is obtained by means of Cayley – Dickson process from its associative division subalgebra and can be represented as a direct sum C = V ⊕ aV.

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Biografía del autor/a

Gangireddy Lakshmi Devi, Jawaharlal Nehru Technological University Ananthapur A.P. India.

Mathematics

Citas

I. Bajo,Lie algebras admitting nonsingular pre-derivations, Indag. Math(N.S)8(1997), 433- 437.

J. Bergen, I. Herstein and C. Lanski,Derivations with invertible values, Canad. J. Math 35(1983), 300-310.

J. Bergen and L. Carini, Derivations with invertible values on a Lie ideal, Canad. Math. Bull 31(1988), 103-110.

J.C. Chang, α-derivations with invertible values, Bull. Inst. Math. Acad. Sinica 13(1985), 323-333.

C. Demir, E. Albas, N. Argac and A. Fosner, Superderivations with invertible values, J. Algebra Appl 14(2015), 11pp.

A. Elduque and H.C. Myung, On flexible Composition algebras, Comm. Algebra 21(1993), 2481-2505.

A. Elduque and H.C. Myung, Flexible Composition algebras and Okubo algebras, Comm. Algebra 19(1991), 1197-1227.

A. Giambruno, P. Misso and P.C. Milies, Derivations with invertible values in rings with involution, Pac.J. Math 123(1986), 47-54.

M. Hongan and H. Komatsu, (σ, τ)-Derivations with invertible values, Bull. Inst. Math. Acad. Sinica 15(1987), 411-415.

I. Kaygorodov and Y. Popov,Alternative algebras admitting derivations with invertible values and invertible derivations, Izvestiya. Math 78(2014), 922-935.

I. Kaygorodov, A. Lopatin and Y. Popov, Jordan algebras admitting derivations with invertible values, arXiv: 1511.00742.

H. Komatsu and A. Nakajima, Generalized derivations with invertible values, Comm. Algebra 32(2004), 1937-1944.

A.A. Popov,Differentiably simple alternative algebras, Algebra and Logic 49(2010), 456-469.

K.A. Zhevlakov, A.M. Slinko, I.P. Shestakov and A.I. Shirshov, Rings that are nearly associative, Pure and Applied Mathematics, 104, Academic Press, Inc, New York-London, 1982.