Let (K, M) be a linear matrix problem induced from a finite dimensional algebra Λ. Then an n×n matrix M in R(K, M) is indecomposable if and only if the number of links in the canonical form M(∞) of M is equal to M-dimn-1. On the other hand, the dimension of the endomorphism ring of M is equal to K-dimn-σ(M).
An embedding from a group algebra to a matrix algebra is given in this paper. By using it, a criterion for an invertible element in a group algebra is proven.
In this paper we improve the character approach to the multiplier conjecture that we presented after 1992, and thus we have made considerable progress in the case of n=3n1. We prove that in the case of n = 3n1 Second multiplier theorem remains true if the assumption 'n1 ＞λ' is replaced by '(n1, λ)=1'.Consequentially we prove that if we let D be a (v, κ,λ)-difference set in an abelian group G, and n=3pr for some prime p, (p,v)=1, then p is a numerical multiplier of D.
