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On Lie Ideals With Generalized Derivations
Siberian Mathematical Journal, 2006Summary: Let \(R\) be a prime ring with characteristic different from 2, let \(U\) be a nonzero Lie ideal of \(R\), and let \(f\) be a generalized derivation associated with \(d\). We prove the following results: (i) If \(a\in R\) and \([a,f(U)]=0\) then \(a\in Z\) or \(d(a)=0\) or \(U\subset Z\); (ii) If \(f^2(U)=0\) then \(U\subset Z\); (iii) If \(u ...
Goelbasi, Oe., Kaya, K.
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Fuzzy Lie Ideals and Fuzzy Lie Subalgebras
Fuzzy Sets and Systems, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chung-Gook Kim, Dong-Soo Lee
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Representations Subduced on an Ideal of a Lie Algebra
Canadian Journal of Mathematics, 1962 This paper considers the properties of the representation of a Lie algebra when restricted to an ideal, the subduced* representation of the ideal. This point of view leads to new forms for irreducible representations of Lie algebras, once the concept of matrices of invariance is developed.
B. Noonan
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Canadian Mathematical Bulletin, 1988
AbstractIn this paper we prove the following result: let R be a prime ring with no non-zero nil left ideals whose characteristic is different from 2 and let U be a non central Lie ideal of R.If d ≠ 0 is a derivation of R such that d(u) is invertible or nilpotent for all u ∈ U, then either R is a division ring or R is the 2 X 2 matrices over a division ...
Mauceri, Silvana, Misso, Paola
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AbstractIn this paper we prove the following result: let R be a prime ring with no non-zero nil left ideals whose characteristic is different from 2 and let U be a non central Lie ideal of R.If d ≠ 0 is a derivation of R such that d(u) is invertible or nilpotent for all u ∈ U, then either R is a division ring or R is the 2 X 2 matrices over a division ...
Mauceri, Silvana, Misso, Paola
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Journal of Intelligent & Fuzzy Systems, 2020
In this paper, we introduce a new definition for nilpotent fuzzy Lie ideal, which is a well-defined extension of nilpotent Lie ideal in Lie algebras, and we name it a good nilpotent fuzzy Lie ideal .
E. Mohammadzadeh +3 more
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In this paper, we introduce a new definition for nilpotent fuzzy Lie ideal, which is a well-defined extension of nilpotent Lie ideal in Lie algebras, and we name it a good nilpotent fuzzy Lie ideal .
E. Mohammadzadeh +3 more
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Ideal hydrodynamics on Lie groups
Physica D: Nonlinear Phenomena, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Ideals of a Lie Algebra of Derivations
Journal of the London Mathematical Society, 1986The most appropriate review of this paper would be to give the first two paragraphs of the author's section 1 (introduction): ''The main theorem of this paper gives a sufficient condition for a Lie algebra of derivations of a commutative associative algebra to be simple.
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On Lie derivations of Lie ideals of prime algebras
Israel Journal of Mathematics, 2001Let \(A\) be a prime associative algebra over a commutative ring with \(1\), let \(L\) be a noncentral Lie ideal of \(A\) with center \(Z(L)\), and let \(\overline L=L/Z(L)\) be the factor Lie algebra. Under some mild technical assumptions (namely, \(\text{char}(A)\neq 2\) and \(A\) does not satisfy \(S_{14}\), the standard polynomial identity of ...
Beidar, K. I., Chebotar, M. A.
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Lie Ideals in Associative Algebras
Canadian Mathematical Bulletin, 1984AbstractIt is shown that in a certain extensive class of algebras one can associate with each Lie ideal a corresponding associative ideal which facilitates the study of Lie ideals, especially for simple algebras. We apply this construction to obtain new, simpler proofs of some known results of Herstein [10] and others on the Lie structure of ...
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Lie superhomomorphisms on Lie ideals in superalgebras
Israel Journal of Mathematics, 2013In this paper the author investigates Lie superhomomorphisms from a Lie ideal of the skew elements of a superalgebra with superinvolution into a unital superalgebra. As a consequence a well-known result on Lie isomorphisms [\textit{K. I. Beidar} et al., Trans. Am. Math. Soc. 353, No.
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