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We show that in a prime nonassociative Novikov algebra every nonzero ideal is non-associative. We prove that Baer (and Andrunakievich) radical and the largest left quasiregular ideal coincide in finite dimensional Novikov algebras over a field of characteristic 0 or algebraically closed field of odd characteristic. We show non-existence of right quasiregular radical in finite dimensional Novikov algebras. [ABSTRACT FROM AUTHOR]

Let A be a unital prime *-algebra with characteristic not 2 and with a projection e ≠ 0 , 1 . Suppose that d : A → Q s (A) is a map satisfying d (x y * z + z y * x 2) = d (x) y * z + x d (y) * z + x y * d (z) + d (z) y * x + z d (y) * x + z y * d (x) 2 for all x , y , z ∈ A , where Q s (A) denotes the symmetric Martindale algebra of quotients of A. It is shown that d is an additive triple derivation. Moreover, there exist a ∈ Q s (A) with a * = − a and an additive *-derivation δ : A → Q s (A) such that d (x) = a x + δ (x) for all x ∈ A . The analogous results for prime locally matrix *-algebras, prime *-algebras with nonzero socle, factor von Neumann algebras and standard operator *-algebras on Hilbert spaces are also described. [ABSTRACT FROM AUTHOR]

We study prime and semiprime Novikov algebras. We prove that prime nonassociative Novikov algebra has zero nucleus and center. It is well known that an ideal of an alternative semiprime algebra is semiprime algebra. We proved this statement for Novikov algebras. It implies that a Baer radical exists in a class of Novikov algebras. [ABSTRACT FROM AUTHOR]

We prove that each -isotope of a prime nonassociative -algebra is a -algebra if and only if the element lies in the commutative center. Every central -isotope of a -monster is demonstrated to be isomorphic to the monster. [ABSTRACT FROM AUTHOR]

We study the overalgebras and the ideals of the Jordan algebras possessing prime (−1, 1)-envelopings. If a Jordan algebra possesses a prime nonassociative (−1, 1)-enveloping then we prove that it is also prime; furthermore, its every ideal is a prime algebra. In particular, the overalgebras and metaideals of Jordan monsters are prime. [ABSTRACT FROM AUTHOR]

Alternative just infinite-dimensional algebras are studied, i.e., infinite-dimensional algebras in which every nonzero ideal has finite codimension. It is proved that these algebras are prime. In the nonassociative case, the Noetherian property with respect to one-sided ideals is proved, and the cases of Cayley-Dickson rings and exceptional algebras are investigated. [ABSTRACT FROM AUTHOR]

We construct some examples of prime Jordan superalgebras of vector type whose odd part is a finitely generated projective module of rank 1 with arbitrarily many generators. These provide some examples of prime Jordan superalgebras of Cheng-Kac type. [ABSTRACT FROM AUTHOR]

Abstract: We show that the algebra of derivations of a strongly nondegenerate Lie algebra L graded by an ordered group G with a finite grading (and satisfying a mild technical condition) inherits the grading from L, i.e., , which turns out to be a strongly nondegenerate Lie algebra, is G-graded and its support has the same length as that of L. This result follows by considering as a subalgebra of the graded maximal algebra of quotients of the Lie algebra L. We specialize the result when L is a Lie algebra of the form or , for A a semiprime associative algebra, K the Lie algebra of the skew elements of a semiprime associative algebra with involution, and and their respective centers. [Copyright &y& Elsevier]

Let G be a monoid with unity e and cancellation, let ℱ be a commutative ring with 1, and let be a G-graded ℱ-semiprime algebra with finite G-grading satisfying a G-graded generalized polynomial identity (with an antiautomorphism when G is commutative) over ℛ e . If ℛ e is prime, then ℛ has a strict GPI over ℛ e . [ABSTRACT FROM PUBLISHER]

Abstract: We describe subalgebras of the Lie algebra that contain all inner derivations of (where and F is an algebraically closed field of characteristic 0). In a more general context where A is a prime algebra satisfying certain technical restrictions, we establish a density theorem for the associative algebra generated by all inner derivations of A. [Copyright &y& Elsevier]

Abstract: Let be an algebra and let be a multilinear polynomial in noncommuting indeterminates . We consider the problem of describing linear maps that preserve zeros of f. Under certain technical restrictions we solve the problem for general polynomials f in the case where We also consider quite general algebras , but only for specific polynomials f. [Copyright &y& Elsevier]

Abstract: We characterize generalized Lie derivations on skew elements of prime algebras with involution, provided that does not satisfy polynomial identities of low degree. The analogous result for matrix algebras is also described. [Copyright &y& Elsevier]

For prime algebras, we describe a linear map which behaves like a left derivation on a fixed multilinear polynomial in noncommuting indeterminates and, in particular, we characterize left derivations by their action on mth powers. [ABSTRACT FROM AUTHOR]

We deal with adjoint commutator and Jordan algebras of isotopes of prime strictly ( −1 , 1)-algebras. It is proved that a system of identities of the form [ x1, x2, x2, x3,..., x n] for n = 2 ,.... , 5 is discernible on isotopes of prime (−1, 1)-algebras. Also it is shown that adjoint Jordan algebras for suitable isotopes of prime (−1, 1)-algebras may possess distinct sets of identities. In particular, isotopes of a prime Jordan monster have different sets of identities in general. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we explore graded algebras of quotients of Lie algebras with special emphasis on the 3-graded case and answer some natural questions concerning its relation to maximal Jordan systems of quotients. [Copyright &y& Elsevier]

By testing quotient rings, we give another viewpoint concerning the relationship between PI and Goldie properties, etc., and f-radical extensions of rings. The main result proved here is as follows: Let R be a prime algebra without nonzero nil right ideals. Suppose that R is f-radical over a subalgebra A, where f(X1,..., Xt) is a multilinear polynomial, not an identity for p × p matrices in case char R = p > 0. Suppose that f is not power-central valued in R. Then the maximal ring of right (left) quotients of A coincides with that of R. Moreover, R is right Goldie if and only if A is. [ABSTRACT FROM AUTHOR]

Let A be a semiprime associative algebra with an involution ∗ over a field of characteristic not 2, let KA be the Lie algebra of all skew elements of A, and let ZKA denote the annihilator of KA. The aim of this paper is to prove that if Q is a ∗-subalgebra of Qs(A) (the Martindale symmetric algebra of quotients of A) containing A, then KQ/ZKQ is a Lie algebra of quotients of KA/ZKA. Similarly, [KQ, KQ]/Z[KQ,KQ] is a Lie algebra of quotients of [KA,KA]/Z[KA,KA]. [ABSTRACT FROM AUTHOR]

Abstract: Let be a prime algebra of characteristic not 2 with extended centroid , let be a noncentral Lie ideal of and let be the subalgebra of generated by . If are linear maps satisfying thatthen there exist a generalized derivation and a linear map such that for all and provided that does not satisfy the standard identity of degree 18. [Copyright &y& Elsevier]

We prove that every exceptional prime alternative algebra satisfies the Engel identity [[ x, y], y] = 0 of index 2. [ABSTRACT FROM AUTHOR]

We prove nilpotency of the alternator ideal of a finitely generated binary $(-1,1)$-algebra. An algebra is a binary $(-1,1)$-algebra if its every 2-generated subalgebra is an algebra of type $(-1,1)$. While proving the main theorem we obtain various consequences: a prime finitely generated binary $(-1,1)$-algebra is alternative; the Mikheev radical of an arbitrary binary $(-1,1)$-algebra coincides with the locally nilpotent radical; a simple binary $(-1,1)$-algebra is alternative; the radical of a free finitely generated binary $(-1,1)$-algebra is solvable. Moreover, from the main result we derive nilpotency of the radical of a finitely generated binary $(-1,1)$-algebra with an essential identity. [ABSTRACT FROM AUTHOR]

In this note we improve the constant of ultraprimeness for the Euclidean algebra of hermitian operators on a quaternionic Hilbert space. More precisely we shall prove that a constant of ultraprimeness is √ of 2−1. [Copyright &y& Elsevier]

It is proved that a finitely generated prime monomial algebra either is primitive or it satisfies a polynomial identity or it is not semiprimitive. This confirms a conjecture of Bell and Smoktunowicz. [ABSTRACT FROM AUTHOR]