On the relational basis of Cayley’s theorem and of similar representations for algebras

Sedaghat, Hassan

doi:10.1090/S0002-9947-1995-1286006-4

On the relational basis of Cayley’s theorem and of similar representations for algebras
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by Hassan Sedaghat

Trans. Amer. Math. Soc. 347 (1995), 3053-3060

DOI: https://doi.org/10.1090/S0002-9947-1995-1286006-4

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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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