The problem of when the k-subdirect sum of a doubly diagonally dominant matrix (DDD matrix) is also a DDD matrix is studied. Some sufficient conditions are given. The same situation is analyzed for diagonally dominant matrices and strictly diagonally dominant matrices. Additionally, some conditions are also derived when card(S)>card(S1) which was not studied by Bru, Pedroche and Szyld [Electron...

A finite lattice is representable if it is isomorphic to the congruence lattice of a finite algebra. In this paper, we develop methods by which we can construct new representable lattices from known ones. The techniques we employ are sufficient to show that every finite lattice which contains no three element antichains is representable. We then show that if an order polynomially complete latti...

Let Γ be a limit group, S ⊂ Γ a subgroup, and N the normaliser of S. If H1(S,Q) has finite Q-dimension, then S is finitely generated and either N/S is finite or N is abelian. This result has applications to the study of subdirect products of limit groups. Limit groups (or ω-residually free groups) have received a good deal of attention in recent years, primarily due to the groundbreaking work o...

Suppose <? denotes a class of totally ordered groups closed under taking subgroups and quotients by o-homomorphisms. We study the following classes: (1) Res (£?), the class of all lattice-ordered groups which are subdirect products of groups in C; (2) Hyp(C), the class of lattice-ordered groups in Res(C) having all their ¿-homomorphic images in Res(<?); Para(C), the class of lattice-ordered gro...