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2-local Jordan automorphisms on operator algebras

Ajda Fošner (2012)

Studia Mathematica

We investigate 2-local Jordan automorphisms on operator algebras. In particular, we show that every 2-local Jordan automorphism of the algebra of all n× n real or complex matrices is either an automorphism or an anti-automorphism. The same is true for 2-local Jordan automorphisms of any subalgebra of ℬ which contains the ideal of all compact operators on X, where X is a real or complex separable Banach spaces and ℬ is the algebra of all bounded linear operators on X.

A Kleinecke-Shirokov type condition with Jordan automorphisms

Matej Brešar, Ajda Fošner, Maja Fošner (2001)

Studia Mathematica

Let φ be a Jordan automorphism of an algebra . The situation when an element a ∈ satisfies 1 / 2 ( φ ( a ) + φ - 1 ( a ) ) = a is considered. The result which we obtain implies the Kleinecke-Shirokov theorem and Jacobson’s lemma.

An extension of Zassenhaus' theorem on endomorphism rings

Manfred Dugas, Rüdiger Göbel (2007)

Fundamenta Mathematicae

Let R be a ring with identity such that R⁺, the additive group of R, is torsion-free. If there is some R-module M such that R M R ( = R ) and E n d ( M ) = R , we call R a Zassenhaus ring. Hans Zassenhaus showed in 1967 that whenever R⁺ is free of finite rank, then R is a Zassenhaus ring. We will show that if R⁺ is free of countable rank and each element of R is algebraic over ℚ, then R is a Zassenhaus ring. We will give an example showing that this restriction on R is needed. Moreover, we will show that a ring due to A....

An identity related to centralizers in semiprime rings

Joso Vukman (1999)

Commentationes Mathematicae Universitatis Carolinae

The purpose of this paper is to prove the following result: Let R be a 2 -torsion free semiprime ring and let T : R R be an additive mapping, such that 2 T ( x 2 ) = T ( x ) x + x T ( x ) holds for all x R . In this case T is left and right centralizer.

A-Rings

Manfred Dugas, Shalom Feigelstock (2003)

Colloquium Mathematicae

A ring R is called an E-ring if every endomorphism of R⁺, the additive group of R, is multiplication on the left by an element of R. This is a well known notion in the theory of abelian groups. We want to change the "E" as in endomorphisms to an "A" as in automorphisms: We define a ring to be an A-ring if every automorphism of R⁺ is multiplication on the left by some element of R. We show that many torsion-free finite rank (tffr) A-rings are actually E-rings. While we have an example of a mixed...

Automorphisms of completely primary finite rings of characteristic p

Chiteng'a John Chikunji (2008)

Colloquium Mathematicae

A completely primary ring is a ring R with identity 1 ≠ 0 whose subset of zero-divisors forms the unique maximal ideal . We determine the structure of the group of automorphisms Aut(R) of a completely primary finite ring R of characteristic p, such that if is the Jacobson radical of R, then ³ = (0), ² ≠ (0), the annihilator of coincides with ² and R / G F ( p r ) , the finite field of p r elements, for any prime p and any positive integer r.

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