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P ( r , m ) near-rings.

Balakrishnan, R., Suryanarayanan, S. (2000)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Polynomial identities of nil algebras of bounded index

Francesca Benanti, Vesselin Drensky (1999)

Bollettino dell'Unione Matematica Italiana

Lo scopo di questo lavoro è di dare una nuova descrizione del T -ideale generato dalla nil-identità x n = 0 come immagine omeomorfa della n -esima potenza tensoriale simmetrica dell'algebra associativa libera K ⁢ X su un campo K di caratteristica 0 . Come applicazione calcoliamo il carattere delle conseguenze multilineari di grado ≤ n + 2 dell'identità x n = 0 .

Posner's second theorem and annihilator conditions with generalized skew derivations

Vincenzo De Filippis, Feng Wei (2012)

Colloquium Mathematicae

Let be a prime ring of characteristic different from 2, r be its right Martindale quotient ring and be its extended centroid. Suppose that is a non-zero generalized skew derivation of and f(x₁,..., xₙ) is a non-central multilinear polynomial over with n non-commuting variables. If there exists a non-zero element a of such that a[ (f(r₁,..., rₙ)),f(r₁, ..., rₙ)] = 0 for all r₁, ..., rₙ ∈ , then one of the following holds: (a) there exists λ ∈ such that (x) = λx for all x ∈ ; (b) there exist q ∈ r and...

Prime and semiprime rings with symmetric skew n-derivations

Ajda Fošner (2014)

Colloquium Mathematicae

Let n ≥ 3 be a positive integer. We study symmetric skew n-derivations of prime and semiprime rings and prove that under some certain conditions a prime ring with a nonzero symmetric skew n-derivation has to be commutative.

Prime modules.

John Dauns (1978)

Journal für die reine und angewandte Mathematik

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