Jordan left derivations in full and upper triangular matrix rings.
We study Jordan (θ,θ)-superderivations and Jordan triple (θ,θ)-superderivations of superalgebras, using the theory of functional identities in superalgebras. As a consequence, we prove that if A = A₀ ⊕ A₁ is a prime superalgebra with deg(A₁) ≥ 9, then Jordan superderivations and Jordan triple superderivations of A are superderivations of A, and generalized Jordan superderivations and generalized Jordan triple superderivations of A are generalized superderivations of A.
Soit un anneau principal et un -module de torsion de type fini. Nous donnons une preuve élémentaire du fait que tout automorphisme de -algèbre de est intérieur.
A ring is called a left APP-ring if the left annihilator is right -unital as an ideal of for any element . We consider left APP-property of the skew formal power series ring where is a ring automorphism of . It is shown that if is a ring satisfying descending chain condition on right annihilators then is left APP if and only if for any sequence of elements of the ideal
Let be the polynomial ring over a ring with unity. A polynomial is referred to as a left annihilating content polynomial (left ACP) if there exist an element and a polynomial such that and is not a right zero-divisor polynomial in . A ring is referred to as left EM if each polynomial is a left ACP. We observe the structure of left EM rings with various properties, and study the relationships between the one-sided EM condition and other standard ring theoretic conditions. Moreover,...
Let K be a field and Γ a finite quiver without oriented cycles. Let Λ := K(Γ,ρ) be the quotient algebra of the path algebra KΓ by the ideal generated by ρ, and let 𝒟(Λ) be the dual extension of Λ. We prove that each Lie derivation of 𝒟(Λ) is of the standard form.