Search Results

You are looking at 1 - 10 of 49 items for :

  • "distributivity" x
  • Mathematics and Statistics x
  • Refine by Access: All Content x
Clear All

We assume the reader is familiar with basic notions of lattice theory and of universal algebra. A small portion of [ 9 ] is sufficient as a prerequisite. A lattice is distributive if and only if it satisfies the identity α ( β + γ ) ≤ α β + γ . It

Restricted access

Summary  

It is shown that, if two bounded distributive lattices satisfy the join-infinite distributive law (JID), then their coproduct also satisfies this law. In 1986, Yaqub proved that generalized Post algebras with a finite lattice of constants satisfy JID, and stated that, in general, it is not known whether a generalized Post algebra satisfies JID when its lattice of constants satisfies JID. In this note, the statement is proved.

Restricted access

. C ., and Koh , K. M . On the length of the lattice of sublattices of a finite distributive lattice . Algebra Universalis 15 , 2 ( 1982 ), 233 – 241 . [6] Chen , C. C ., Koh , K. M ., and Teo , K. L . On the sublattice-lattice of a

Open access

Abstract  

The relationship between absolute retracts, injectives and equationally compact algebras in finitely generated congruence distributive varieties with 1- element subalgebras is considered and several characterization theorems are proven. Amongst others, we prove that the absolute retracts in such a variety are precisely the injectives in the amalgamation class and that every equationally compact reduced power of a finite absolute retract is an absolute retract. We also show that any elementary amalgamation class is Horn if and only if it is closed under finite direct products.

Restricted access

LetS be a 0-distributive semilattice and be its minimal spectrum. It is shown that is Hausdorff. The compactness of has been characterized in several ways. A representation theorem (like Stone's theorem for Boolean algebras) for disjunctive, 0-distributive semilattices is obtained.

Restricted access

Abstract  

We prove that the tolerance lattice TolA of an algebra A from a congruence modular variety V is 0-1 modular and satisfies the general disjointness property. If V is congruence distributive, then the lattice Tol A is pseudocomplemented. If V admits a majority term, then Tol A is 0-modular.

Restricted access
Restricted access
Restricted access