A Field Guide to Equational Logic

GEORGE F. McNULTYDepartment of Mathematics, University of South CarolinaColumbia, SC 29208, USA(mcnultyOmilo. math. sarolina. edu)(Received 12 May 1992)1. IntroductionThe concepts that can be expressed by means of equations and the kinds of proofs thatmay be devised using equations are central concerns of equational logic. The concept ofa ring is ordinarily presented by saying that a ring is a system (R, +, -, ,0,1) in whichthe following equations are true:A ring is an algebra-meaning here a nonempty set endowed with a system of finitaryoperations. Equations, on the other hand, are certain strings of formal symbols. Theconcept of truth establishes a binary relation between equations and algebras: an equations ;t; t is

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