Browsing by Author "2360b97e-7600-4aaa-a174-f5dec1c1dc64"
Now showing items 1-7 of 7
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(2007)We study commutative algebras which are generalizations of Jordan algebras. The associator is defined as usual by (x, y, z) = (x y)z - x(y z). The Jordan identity is (x2, y, x) = 0. In the three generalizations given below, ...
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(2011)This paper deals with two varieties of commutative non-associative algebras. One variety satisfies Lx3+Lx3=0. The other variety satisfies Lx3=0. We prove that in either variety, any finitely generated algebra is nilpotent. ...
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(2007)We extend the concept of commutative nilalgebras to commutative algebras which are not power associative. We shall study commutative algebras A over fields of characteristic ≠ 2, 3 which satisfy the identities x(x(xx)) = ...
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(2005)We shall study representations of algebras over fields of characteristic ≠ 2, 3 of dimension 4 which satisfy the identities xy - yx = 0, and ((xx)x)x = 0. In these algebras the multiplication operator was shown to be ...
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(2002)We study conditions under which the identity ((xx)x)x = 0 in a commutative nonassociative algebra A implies Rx is nil-potent where Rx is the multiplication operator Rx(y) = xy for all y in A. The separate conditions that ...
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(2008)In this article we study nonassociative rings satisfying the polynomial identity x(yz)=y(zx), which we call "cyclic rings." We prove that every semiprime cyclic ring is associative and commutative and that every cyclic ...
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(Universidad Catolica del Norte, 2010)We study commutative right-nilalgebras of right-nilindex four satisfying the identity (b(aa))a = b((aa)a). Ourmainresultisthatthese algebras are solvable and not necessarily nilpotent. Our results require characteristic 6≠2, 3, 5.
