Lattice Algebra Research Articles

Banach f-algebras and Banach lattice algebras with unit

We give a necessary and sufficient condition for a Banach lattice algebra to be representable as a Banach lattice of continuous realvalued functions on a compact space, endowed with the pointwise defined multiplication. Moreover, we give a characterisation of Banach lattice algebras possessing an algebraic unit.

An Algebraic Description of Stereochemical Correspondence

It is shown that a stereochemical correspondence between two molecular systems can be represented by a commuting diagram of the point groups and permutation groups involved. The effect of the diagrammatic condition on the mappings of the cosets, double cosets, subgroup lattice, and double coset algebra determined for the two molecular systems by point group to permutation group homomorphisms is detailed. Chemical similarities implied by a stereochemical correspondence are indicated, and six examples are provided and discussed.

A note on the mathematical basis of the SLIC index

AbstractIt has been shown that the index entries generated by the SLIC technique constitute a lattice which is a subset of the power set of the set of descriptors assigned to a document and that this fact leads to an improved algorithm for generating SLIC entries. It has also been shown that an isomorphic mapping exists between the SLIC lattice and a Boolean lattice (algebra).

Lattice isomorphic solvable Lie algebras

Let L be a Lie algebra over a field κ of any characteristic, and consider the lattice ℒ(L) of all subalgebras of L. In this paper we prove that if L and M are lattice isomorphic Lie algebras, over a field of any characteristic, and L′ and M′ are nilpotent, then the difference between the orders of solvability of L and M differs by at most one.

The theory of switching nets

The paper develops a strictly mathematical, unified theory of combinational switching networks, with the aid of linear graph theory and lattice algebra. The theory is based on the concept of a lattice-weighted, directed linear graph, termed switching net. The advantages of using lattice algebra, rather than Boolean algebra are emphasized. A calculus of lattice matrices is outlined in Section II, and then applied to the study of switching nets (Section III). A suitable formulation of Ashenhurst's uniqueness theorem, and a modified version of its proof are given in Section IV. In Section V switching net theory is extended to multi-terminal and reiterative nets, generalizing results due to M.L. Tsetlin and A.Sh. Blokh.

The Theory of Switching Nets

The paper develops a strictly mathematical unified theory of combinational switching networks of various types, with the aid of linear graph theory and lattice algebra. The switching net serves as the basic concept; it is defined as a directed, linear graph, the branches of which are weighted by elements of a distributive lattice. Similarly to the application of Boolean matrix theory to the study of relay-contact networks, the theory of switching nets makes use of a more general lattice matrix calculus. The paper includes, besides some new results, suitably modified, purely mathematical versions of known theorems on electrical contact networks.

Applications of lattice algebra

By a finite lattice† is meant any finite class having the following properties: