\(L\)-algebras in logic, algebra, geometry, and topology
\(L\)-algebras are treated here mainly from the viewpoint of algebraic logic as algebras of kind \((A,\to,1)\) satisfying the axioms \((x \to y) \to (x \to z) = (y \to x) \to (y \to z)\) and \(x \to y = y \to x = 1 \Rightarrow x = y\), cf. [the author, J. Algebra 320, No. 6, 2328--2348 (2008; Zbl 1158.06009)]. The paper is an informal review of \(L\)-algebras, their examples from, and applications in, logic, arithmetics, algebra, analysis, geometry, topology. In particular, discussed are connections of these algebras with hoops and Heyting algebras, and also their relationship to \(\ell\)-groups.
scientific article; zbMATH DE number 7221933
scientific article