Subdirect products of rings and distributive lattices

Distributive Lattices of Jacobson Rings

We characterize the distributive lattices of Jacobson rings and prove that if a semiring is a distributive lattice of Jacobson rings, then, up to isomorphism, it is equal to the subdirect product of a distributive lattice and a Jacobson ring. Also, we give a general method to construct distributive lattices of Jacobson rings.

The Structure of Pseudocomplemented Distributive Lattices. I: Subdirect Decomposition

In this paper all subdirectly irreducible pseudocomplemented distributive lattices are found. This result is used to establish a Stone-like representation theorem conjectured by G. Grätzer and to find all equational subclasses of the class of pseudocomplemented distributive lattices.

A Subdirect-union Representation for Completely Distributive Complete Lattices

4. Proof of Theorem 2. Harish-Chandra [l] and others have proved that every Lie algebra over a field of characteristic zero has a faithful representation. Consequently by Lemma 4, 8 has a faithful representation x—*Qx whose matrices have elements in an algebraic extension $ of g such that t(QxQv) =0 for all x of 31 and all y of 8. We now apply another form of Cartan's criterion for solvability ...

Products of Skeletons of Finite Distributive Lattices

We prove that the skeleton of a product of finitely many finite distributive lattices is isomorphic to the product of skeletons of its factors. Thus, it is possible to construct finite distributive lattices with a given directly reducible skeleton by reducing the problem to the skeleton factors. Although not all possible lattices can be obtained this way, we show that it works for the smallest ...

Subdirect Sums of Rings