Involutive equality algebras
The present paper aims to study a special class of equality algebras, called involutive equality algebra. We obtain some properties of this structure and prove that every linearly ordered 0-compatible equality algebra includes a \((\sim _0)\)-involutive subalgebra. We prove that each \((\sim _0)\)-involutive equality algebra is a lattice, while it is distributive under a suitable condition. Then, we define \((\sim _0)\)-involutive deductive systems on bounded equality algebras and represent a condition under which the set of all dense elements of an equality algebra is a \((\sim _0)\)-involutive deductive system. Finally, we find the relations among 0-compatible equality algebras, residuated lattices and Boolean algebras.
KeywordsEquality algebra Involutive equality algebra Residuated lattice Boolean algebra
Mathematics Subject Classification03G25 06F05 06F35
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- Novák V (2007) EQ-Algebras in progress. In: Castillo O, Melin P, Ross OM, Sepúlveda Cruz R, Pedrycz W, Kacprzyk J (eds) Theoretical advances and applications of fuzzy logic and soft computing. Advances in Soft Computing, vol 42. Springer, Berlin, HeidelbergGoogle Scholar