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Ruth Nascimento Ferreira

Publications and source records attributed to Ruth Nascimento Ferreira.

4 recordsLinked to original sources
arXiv2021

$*$-Lie-type maps on $C^*$-algebras

Let $\mathfrak{A}$ and $\mathfrak{A}'$ be two $C^*$-algebras with identities $I_{\mathfrak{A}}$ and $I_{\mathfrak{A}'}$, respectively, and $P_1$ and $P_2 = I_{\mathfrak{A}} - P_1$ nontrivial symmetric projections in $\mathfrak{A}$. In this paper we study the characterization of multiplicative $*$-Lie-type maps. In particular, if $\mathcal{M}$ is a factor von Neumann algebra then every complex scalar multiplication bijective unital multiplicative $*$-Lie-type map is $*$-isomorphism.

math.OA↗
arXiv2021

Additivity of $n$-Multiplicative Mappings of Gamma Rings

In this paper, we address the additivity of $n$-multiplicative isomorphisms and $n$-multiplicative derivations on Gamma rings. We proved that, if $\M$ is a $Γ$-ring satisfying the some conditions, then any $n$-multiplicative isomorphism $\left(φ, ϕ\right)$ of $\M$ onto an arbitrary gamma ring is additive.

math.RA↗
arXiv2021

Nonlinear $*$-Jordan-type derivations on alternative $*$-algebras

Let $A$ be an unital alternative $*$-algebra. Assume that $A$ contains a nontrivial symmetric idempotent element $e$ which satisfies $xA \cdot e = 0$ implies $x = 0$ and $xA \cdot (1_A - e) = 0$ implies $x = 0$. In this paper, it is shown that $Φ$ is a nonlinear $*$-Jordan-type derivation on A if and only if $Φ$ is an additive $*$-derivation. As application, we get a result on alternative $W^{*}$-algebras.

math.RA↗
arXiv2018

Generalized Jordan derivations of Incidence Algebras

For a given ring $\mathfrak{R}$ and a locally finite pre-ordered set $(X, \leq)$, consider $I(X, \mathfrak{R})$ to be the incidence algebra of $X$ over $\mathfrak{R}$. Motivated by a Xiao's result which states that every Jordan derivation of $I(X,\mathfrak{R})$ is a derivation in the case $\mathfrak{R}$ is $2$-torsion free, one proves that each generalized Jordan derivation of $I(X,\mathfrak{R})$ is a generalized derivation provided $\mathfrak{R}$ is $2$-torsion free, getting as a consequence the above mentioned result.

math.OA↗