Primitive lattice matrices.(English)Zbl 1057.15021

Summary: Let $$\langle L,\leq,\vee,\wedge\rangle$$ be a distributive lattice. A matrix $$A$$ over the lattice $$L$$ is called a lattice matrix. In this paper, the concepts of primitive lattice matrices are introduced, and some algebraic properties of them are obtained.

MSC:

 15B33 Matrices over special rings (quaternions, finite fields, etc.) 06D05 Structure and representation theory of distributive lattices