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A norm on separable noncommutative Jordan algebras of degree $2$ [PDF]

Proceedings of the American Mathematical Society, 1969
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THE JORDAN DERIVATIONS OF SEMIPRIME RINGS AND NONCOMMUTATIVE BANACH ALGEBRAS

Journal of the Chungcheong Mathematical Society, 2016
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Chang, Ick-Soon: Jordan derivations in noncommutative Banach algebras. (English). - [J] Bull. Korean Math. Soc. 37, No. 3, 429-435 (2000). [ISSN 1015-8634]

, 2004
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On lie algebras associated with nodal noncommutative Jordan algebras

Acta Mathematica Sinica, 1986
The Lie algebra \(A^-_ n\) associated with a simple Lie-admissible nodal noncommutative Jordan algebra \(A_ n\) over a field of characteristic \(p>2\) is studied. It is shown that either \(A^-_ n/\) or its derived algebra is simple of generalized Cartan type H(2r).
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On the socle of a noncommutative Jordan algebra

Manuscripta Mathematica, 1986
Let A be a nondegenerate noncommutative Jordan algebra over a field of characteristic not two. The socle of A is the sum of the minimal inner ideals of A. The authors prove that the socle contains all elements in A of finite rank, that is, all \(b\in A\) such that \(U_ bA\) is finite- dimensional.
Fernández López, Antonio, Rodríguez Palacios, Angel   +1 more
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Noncommutative matrix jordan algebras, cayley-dickson algebras, and schafer's theorem¹

Communications in Algebra, 1995
We provide a construction of noncommutative Jordan algebras of degree two. The construction can be iterated, and we show that after the first few iterations no new derivations arise. The relationship between this iterative process and the Cayley-Dickson process is studied, and the result on deriva¬tions is used to obtain a generalization of Schafer's ...
Robert B. Brown, Nora C. Hopkins
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A Generalization of Degree Two Simple Finite-Dimensional Noncommutative Jordan Algebras

Canadian Journal of Mathematics, 1980
Let be an algebra over a field . For x, y, z in , write (x, y, z) = (xy)z – x(yz) and x-y = xy + yx. The attached algebra is the same vector space as , but the product of x and y is x · y. We aim to prove the following result.THEOREM 1. Let be a finite-dimensional, power-associative, simple algebra of degree two over a field of prime characteristic ...
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Noncommutative Jordan algebras a under the condition that A(+) is associative

Siberian Mathematical Journal, 1992
See the review in Zbl 0753.17003.
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Noncommutative Jordan mutation algebras: A partial order relation

1986
Let A be an associative algebra with 1 over a field of characteristic not 2 (multiplication denoted by juxtaposition), and let p,q be two elements in A. The mutation algebra A(p,q) is then defined as the (nonassociative) algebra over the same underlying linear space as A but with multiplication given by: \(x*y=xpy-yqx.\) The first part of this paper is
González, S., Martínez, C.
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NONCOMMUTATIVE JORDAN RIESZ ALGEBRAS

The Quarterly Journal of Mathematics, 1988
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