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Jordan *-derivation pairs on standard operator algebras and related results

Dilian Yang (2005)

Colloquium Mathematicae

Motivated by Problem 2 in [2], Jordan *-derivation pairs and n-Jordan *-mappings are studied. From the results on these mappings, an affirmative answer to Problem 2 in [2] is given when E = F in (1) or when 𝓐 is unital. For the general case, we prove that every Jordan *-derivation pair is automatically real-linear. Furthermore, a characterization of a non-normal prime *-ring under some mild assumptions and a representation theorem for quasi-quadratic functionals are provided.

Jordan ideals and derivations in prime near-rings

Abdelkarim Boua, Lahcen Oukhtite, Abderrahmane Raji (2014)

Commentationes Mathematicae Universitatis Carolinae

In this paper we investigate 3 -prime near-rings with derivations satisfying certain differential identities on Jordan ideals, and we provide examples to show that the assumed restrictions cannot be relaxed.

Jordan superderivations and Jordan triple superderivations of superalgebras

He Yuan, Liangyun Chen (2016)

Colloquium Mathematicae

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.

Left APP-property of formal power series rings

Zhongkui Liu, Xiao Yan Yang (2008)

Archivum Mathematicum

A ring R is called a left APP-ring if the left annihilator l R ( R a ) is right s -unital as an ideal of R for any element a ∈ R . We consider left APP-property of the skew formal power series ring R [ [ x ; α ] ] where α is a ring automorphism of R . It is shown that if R is a ring satisfying descending chain condition on right annihilators then R [ [ x ; α ] ] is left APP if and only if for any sequence ( b 0 , b 1 , ⋯ ) of elements of R the ideal l R ...

Left EM rings

Jongwook Baeck (2024)

Czechoslovak Mathematical Journal

Let R [ x ] be the polynomial ring over a ring R with unity. A polynomial f ( x ) ∈ R [ x ] is referred to as a left annihilating content polynomial (left ACP) if there exist an element r ∈ R and a polynomial g ( x ) ∈ R [ x ] such that f ( x ) = r g ( x ) and g ( x ) is not a right zero-divisor polynomial in R [ x ] . A ring R is referred to as left EM if each polynomial f ( x ) ∈ R [ x ] 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,...

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