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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.


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...

Automorphism group of representation ring of the weak Hopf algebra H 8 ˜

Dong Su, Shilin Yang (2018)

Czechoslovak Mathematical Journal

Let H 8 be the unique noncommutative and noncocommutative eight dimensional semi-simple Hopf algebra. We first construct a weak Hopf algebra H 8 ˜ based on H 8 , then we investigate the structure of the representation ring of H 8 ˜ . Finally, we prove that the automorphism group of r ( H 8 ˜ ) is just isomorphic to D 6 , where D 6 is the dihedral group with order 12.

Automorphism liftable modules

Chelliah Selvaraj, Sudalaimuthu Santhakumar (2018)

Commentationes Mathematicae Universitatis Carolinae

We introduce the notion of an automorphism liftable module and give a characterization to it. We prove that category equivalence preserves automorphism liftable. Furthermore, we characterize semisimple rings, perfect rings, hereditary rings and quasi-Frobenius rings by properties of automorphism liftable modules. Also, we study automorphism liftable modules with summand sum property (SSP) and summand intersection property (SIP).

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