Hyperidentities in algebras and varieties

ContentsIntroduction ??1. The concept of hyperidentity. Hyperidentities of binary representations1.1. The concept of hyperidentity: examples1.2. Binary Cayley theorems for semigroups, idempotent and commutative semigroups, groups and the multiplicative groups of fields1.3. Stochastic algebras. The concept of coidentity ??2. The category of algebras of the same arithmetic type2.1. Homomorphisms and automorphisms of algebras of the same arithmetic type2.2. Hypervarieties of algebras ??3. The category of systems of the same arithmetic type. Nonclassical semantics in second order language ??4. Non-trivial associative and distributive hyperidentities in algebras that are invertible or close to being invertible Bibliography

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