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Algebra and Logic, 1988
This work is based on the results and methods of the author's earlier study of Jordan \(A\)-algebras [Algebra Logika 26, No. 6, 731--755 (1987; Zbl 0648.17008)]. The term algebra is used when working over a commutative associative ring with \(1/2\), while the term ring is used when working over the integers.
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This work is based on the results and methods of the author's earlier study of Jordan \(A\)-algebras [Algebra Logika 26, No. 6, 731--755 (1987; Zbl 0648.17008)]. The term algebra is used when working over a commutative associative ring with \(1/2\), while the term ring is used when working over the integers.
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Canadian Journal of Mathematics, 1981
In the theory of Jordan algebras one encounters several definitions of the trace, and it is sometimes unclear whether the different notions are equivalent or not. If we restrict attention to the so–called JB–algebras studied in [2] and their weakly closed analogues JBW–algebras [8], we shall in the present note show that the different concepts are all ...
Pedersen, Gert Kjaergard +1 more
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In the theory of Jordan algebras one encounters several definitions of the trace, and it is sometimes unclear whether the different notions are equivalent or not. If we restrict attention to the so–called JB–algebras studied in [2] and their weakly closed analogues JBW–algebras [8], we shall in the present note show that the different concepts are all ...
Pedersen, Gert Kjaergard +1 more
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Jacobi–Jordan-admissible algebras and pre-Jacobi–Jordan algebras
Journal of Algebra and Its ApplicationsThe main purpose of this paper is to study Jacobi–Jordan-admissible algebras and some particular classes like pre-Jacobi–Jordan algebras. First, we provide characterizations of Jacobi–Jordan algebras by means of oxidation process. Then, we discuss Jacobi–Jordan-admissible algebras for which we obtain a surprising characterization as 3-power anti ...
Amir Baklouti +3 more
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Malcev–Poisson–Jordan algebras
Journal of Algebra and Its Applications, 2016Malcev–Poisson–Jordan algebra (MPJ-algebra) is defined to be a vector space endowed with a Malcev bracket and a Jordan structure which are satisfying the Leibniz rule. We describe such algebras in terms of a single bilinear operation, this class strictly contains alternative algebras. For a given Malcev algebra [Formula: see text], it is interesting to
Ait Ben Haddou, Malika +2 more
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Ternary Hom-Jordan algebras induced by Hom-Jordan algebras
Linear and Multilinear Algebra, 2020The purpose of this paper is to study the relationships between a Hom-Jordan algebras and its induced ternary Hom-Jordan algebras.
Arfa, Anja +2 more
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INTEGRATION ON JORDAN ALGEBRAS
Mathematics of the USSR-Izvestiya, 1984See the review in Zbl 0516.46044.
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Siberian Advances in Mathematics, 2019
Summary: We study the variety \(\mathcal{V}_J\) of Jordan algebras defined by the identities \(x^2yx\equiv 0\) and \((x_1y_1)(x_2y_2)(x_3y_3)\equiv 0\). We suggest a method for constructing an algebra in \(\mathcal{V}_J\) from an arbitrary Lie superalgebra. For certain subvarieties, we completely describe their identities and sequences of cocharacters.
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Summary: We study the variety \(\mathcal{V}_J\) of Jordan algebras defined by the identities \(x^2yx\equiv 0\) and \((x_1y_1)(x_2y_2)(x_3y_3)\equiv 0\). We suggest a method for constructing an algebra in \(\mathcal{V}_J\) from an arbitrary Lie superalgebra. For certain subvarieties, we completely describe their identities and sequences of cocharacters.
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Applications of Artificial Intelligence and Machine Learning Algorithms to Crystallization
Chemical Reviews, 2022Christos Xiouras +2 more
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