Nonnegative matrix semigroups with finite diagonals

Nonnegative Matrix Semigroups with Finite Diagonals

Let S be a multiplicative semigroup of matrices with nonnegative entries. Assume that the diagonal entries of the members of S form a finite set. This paper is concerned with the following question: Under what circumstances can we deduce that S itself is finite?

Multiplicative diagonals of matrix semigroups

Finite derivation type for Rees matrix semigroups

This paper introduces the topological finiteness condition finite derivation type (FDT) on the class of semigroups. This notion is naturally extended from the monoid case. With this new concept we are able to prove that if a Rees matrix semigroupM[S; I, J ;P ] has FDT then the semigroup S also has FDT. Given a monoid S and a finitely presented Rees matrix semigroup M[S; I, J ;P ] we prove that ...

Irreducible Matrix Representations of Finite Semigroups

Munn [9] has shown that for a semigroup S satisfying the minimal condition on principal ideals, there is a natural one-to-one correspondence between irreducible representations of S and irreducible representations vanishing at zero of its 0-simple (or simple) principal factors; for the case of S finite, see Ponizovskii [11]. On the other hand, Clifford, [3] and [4], has obtained all representat...

Diagonals of normal operators with finite spectrum.

Let X={lambda1, ..., lambdaN} be a finite set of complex numbers, and let A be a normal operator with spectrum X that acts on a separable Hilbert space H. Relative to a fixed orthonormal basis e1, e2, ... for H, A gives rise to a matrix whose diagonal is a sequence d=(d1, d2, ...) with the property that each of its terms dn belongs to the convex hull of X. Not all sequences with that property c...