On the relational basis of Cayley's theorem and of similar representations for algebras
Trans. Amer. Math. Soc. 347 (1995), 3053-3060
Primary 08A02; Secondary 06A05, 06A12, 06B15, 06F05, 06F25, 08A05, 20M30
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Abstract: 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.
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