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arxiv: 2512.14326 · v2 · submitted 2025-12-16 · 🧮 math.RA · math.LO

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The theory of implicit operations

Luca Carai , Miriam Kurtzhals , Tommaso Moraschini
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classification 🧮 math.RA math.LO
keywords implicitmathsfoperationstheoryalgebraicalgebrasclassdefined
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A family of partial functions of a class of algebras $\mathsf{K}$ is said to be an implicit operation of $\mathsf{K}$ when it is defined by a first order formula and it is preserved by homomorphisms. In this work, we develop the theory of implicit operations from an algebraic standpoint.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A completion of reduced commutative rings

    math.RA 2026-05 accept novelty 7.0

    Adjoining weak inverses and weak prime roots completes reduced commutative rings into a discriminator variety with regular monomorphisms and simple dominion descriptions.

  2. A categorical description of simple Beth companions

    math.CT 2026-05 unverdicted novelty 6.0

    Simple pp expansions of a quasivariety K are precisely the quasivarieties M such that the forgetful functor U from M to K is well-defined and M is isomorphic to a mono-reflective subcategory of K.