ON THE RELATIONAL BASIS OF CAYLEYS THEOREM AND OF SIMILAR REPRESENTATIONS FOR ALGEBRAS

摘要

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 ordered set. An extension of this procedure yields a uniform set of representation theorems for a large class of associative algebras. [References: 4]