On theta-centralizers of semiprime rings

St Petersburg Mathematical Journal, 2009

International Journal of Algebra, 2010

2014

Let m and n be fixed integers with m ≥ 1, n ≥ 1 and let R be a (m + n + 2)!− torsion free semiprime ring with the identity element suppose there exists an additive mapping T : R → R such that T (x m+n+1) = θ(x m)T (x)θ(x n) holds for all x ∈ R where θ is an automorphisms of R. In this case T is a centralizer.

Glasnik Matematicki, 2003

2012

Let R be a semiprime ring equipped with an involution ‘∗’ and let α : R → R be an automorphism of R. An additive mapping T : R −→ R is called a left (resp. right) Jordan α-∗centralizer if for all x ∈ R, T (x2) = T (x)α(x∗) (resp. T (x2) = α(x∗)T (x)). If T is both left and right Jordan α-∗centralizer of R then it is called Jordan α-∗centralizer of R. In the present paper it is shown that an additive mapping T on a 2-torsion free semiprime ring R satisfying 2T (x2) = T (x)α(x∗) + α(x∗)T (x) for all x ∈ R, is a Jordan α-∗centralizer. Mathematics Subject Classification: 16W25, 16N60

ijpam.eu

Abstract: In this paper we show that a mapping T of a semiprime ring R into itself is a centralizer if and only if it is a centralizing left centralizer. We also prove that if T and S are left centralizers of a semiprime ring R satisfying T(x)x + xS(x) ∈ Z(R) (the center of R) for all x ∈ R, then ...

Rocky Mountain Journal of Mathematics, 2011

Análisis y contraste del sistema de selección de la alta magistratura en Honduras, 2023

In the different laws of countries are established schemes to choose the High Judiciary as it is observed in studies among which stand out those carried out by Gutierrez de Colmenarez (2006) and (Guarín et al., 2019). In this context, it is intended to analyze and contrast the new system of selection of the Judiciary adopted by Honduras, using the qualitative approach of juridical research, legal hermeneutics, documentary analysis and Comparative Law. Then, it can be affirmed that there is an evolution about compliance with internationals standards however this was not extensive to the Legislature which continues deciding politically. Consequently, this circumstance is not different from other regional countries but in relation with Italy, it is too simplified. From the analysis it is observed that new processis based on principles that promote the strengthening of the Rule of Law, as well as it is evident that while the Legislature continues to choose the High Judiciary without criteria standardization and discrediting the judicial career it does not represent a deep reform. Regarding the comparative with other legislations there are minimal differences, the only important one is related to the entity that defines the profile of candidates and appoint them.