Jordan homomorphisms and right alternative rings

Jordan homomorphisms and harmonic mappings

We show that each Jordan homomorphism R→ R′ of rings gives rise to a harmonic mapping of one connected component of the projective line over R into the projective line over R′. If there is more than one connected component then this mapping can be extended in various ways to a harmonic mapping which is defined on the entire projective line over R. Mathematics Subject Classification (2000): 51C0...

Jordan * -homomorphisms on C * -algebras

In this paper, we investigate Jordan ∗-homomorphisms on C∗-algebras associated with the following functional inequality ‖f( b−a 3 ) + f( a−3c 3 ) + f( 3a+3c−b 3 )‖ ≤ ‖f(a)‖. We moreover prove the superstability and the generalized Hyers-Ulam stability of Jordan ∗homomorphisms on C∗-algebras associated with the following functional equation f( b− a 3 ) + f( a− 3c 3 ) + f( 3a+ 3c− b 3 ) = f(a).

Approximation of Jordan homomorphisms in Jordan Banach algebras RETRACTED PAPER

In this paper, we investigate the generalized Hyers-Ulam stability of Jordan homomorphisms in Jordan Banach algebras for the functional equation begin{align*} sum_{k=2}^n sum_{i_1=2}^ksum_{i_2=i_{1}+1}^{k+1}cdotssum_{i_n-k+1=i_{n-k}+1}^n fleft(sum_{i=1,i not=i_{1},cdots ,i_{n-k+1}}^n x_{i}-sum_{r=1}^{n-k+1} x_{i_{r}}right) + fleft(sum_{i=1}^{n}x_{i}right)-2^{n-1} f(x_{1}) =0, end{align*} where ...

Right Alternative Division Rings of Characteristic Two

Right Alternative Rings of Characteristic Two

for all w, x, y and showed by example that (1.1) can fail to hold. Prior to this, Kleinfeld [l ] generalized the Skornyakov theorem in another direction by assuming only the absence of one sort of nilpotent element. We now specify Kleinfeld's result in detail. Let F be the free nonassociative ring generated by Xi and x2 and suppose that R is any right alternative ring. Kleinfeld calls t, u, v i...