Characterizations of a commutative semisimple modular annihilator Banach algebra through its socle

Jordan Automorphisms on a Semisimple Banach Algebra

In the group of (continuous) Jordan automorphisms, with the uniform topology, on a semisimple Banach algebra, we show that the connected component of the identity consists of automorphisms. P. Civin and B. Yood have shown that a Jordan homomorphism (that is, a homomorphism that preserves the product xoy = | (xy+yx)) from a Banach algebra onto a semisimple Banach algebra is continuous provided t...

Elements in a Commutative Banach Algebra Determining the Norm Topology

For an element a of a commutative complex Banach algebra (A, ‖ · ‖) we investigate the following property: every complete norm | · | on A making the multiplication by a from (A, | · |) to itself continuous is equivalent to ‖ · ‖.

The annihilator-inclusion Ideal graph of a commutative ring

Let R be a commutative ring with non-zero identity. The annihilator-inclusion ideal graph of R , denoted by ξR, is a graph whose vertex set is the of allnon-zero proper ideals of $R$ and two distinct vertices $I$ and $J$ are adjacentif and only if either Ann(I) ⊆ J or Ann(J) ⊆ I. In this paper, we investigate the basicproperties of the graph ξR. In particular, we showthat ξR is a connected grap...

Commutative Algebra Commutative Algebra : General

Weak amenability of (2N)-th dual of a Banach algebra

In this paper by using some conditions, we show that the weak amenability of (2n)-th dual of a Banach algebra A for some $ngeq 1$ implies the weak amenability of A.