Considering a binary operation as a ternary relation permits certain sections of the latter (which are functions) to be used in representing an abstract semigroup as a family of the self-maps of its underlying set under function composition. The idea is thus seen to be entirely similar to the way that the sections of a partial ordering under set inclusion represent the (abstract) partially orde...

We investigate commutator operations on compatible uniformities. We define a commutator operation for uniformities in the congruence-modular case which extends the commutator on congruences, and explore its properties. Introduction The purpose of this paper is to generalize the commutator of congruences to a commutator of compatible uniformities. Commutator theory (on congruences) works best fo...

We investigate commutator operations on compatible uniformities. We present a commutator operation for uniformities in the congruence-modular case which extends the commutator on congruences, and explore its properties. Introduction The purpose of this paper is to generalize the commutator of congruences to a commutator of compatible uniformities. Commutator theory (on congruences) works best f...

A class of algebras is said to be globally determined if any two members of that class having isomorphic power algebras are isomorphic. In 1984, Y. Kobayashi proved that semilattices are globally determined. By using his methods, we prove that the class of all ∗-bands has the same property. Let 〈A,F〉 be a universal algebra. Clearly, the operations from F can be extended to the collection of all...

Vaughan Pratt has introduced objects consisting of pairs (A, W ) where A is a set and W a set of subsets of A, such that (i) W contains ∅ and A, (ii) if C is a subset of A×A such that for every a ∈ A, both {b | (a, b) ∈ C} and {b | (b, a) ∈ C} are members of W (a “crossword” with all “rows” and “columns” in W ), then {b | (b, b) ∈ C} (the “diagonal word”) also belongs to W, and (iii) for all di...

We define an axiom system for rounded arithmetic to be complete if we can recover from any model of the axioms the exact algebra from whence it came. A complete set of axioms is given for rounded addition and multiplication. In some circles of numerical analysis, there is a deep suspicion that some of the scientific and engineering calculations being done by computer do not correspond to extern...