Single elements of matrix incidence algebras

Generators of matrix incidence algebras

Let n E Z+ and let K be a field. Let ~ be a partial order on {1, 2, ... , n}. Let An(:::;) be the matrix incidence algebra consisting of those n x n matrices A = (ai,j) with entries in K, satisfying ai,j 0 whenever i 1:. j. For a subset £ ~ An (::5), a necessary and sufficient condition that the algebra generated by £ u {I} is An(::5) is that (i) for every 1 :::; i, j :::; n with i =1= j, there...

Single Elements of Finite Csl Algebras

An element s of an (abstract) algebra A is a single element of A if asb = 0 and a, b ∈ A imply that as = 0 or sb = 0. Let X be a real or complex reflexive Banach space, and let B be a finite atomic Boolean subspace lattice on X, with the property that the vector sum K +L is closed, for every K,L ∈ B. For any subspace lattice D ⊆ B the single elements of Alg D are characterised in terms of a coo...

NILPOTENT GRAPHS OF MATRIX ALGEBRAS

Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...

Finding splitting elements and maximal tori in matrix algebras

amenability of banach algebras

chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...