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Hopf monoids in varieties
Commutative varieties provide a natural setting for generalizing Hopf algebra theory over commutative rings, since they satisfy the various...
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A uniform Birkhoff theorem
Birkhoff’s HSP theorem characterizes the classes of models of algebraic theories as those being closed with respect to homomorphic images,...
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Involutive Residuated Lattices Based on Modular and Distributive Lattices
An involutive residuated lattice (IRL) is a lattice-ordered monoid possessing residual operations and a dualizing element. We show that a large class...
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Tolerances as images of congruences in varieties defined by linear identities
An identity s = t is linear if each variable occurs at most once in each of the terms s and t . Let T be a tolerance relation of an algebra
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Representable tolerances in varieties
We discuss two possible ways of representing tolerances: first, as a homomorphic image of some congruence; second, as the relational composition of...
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Independent joins of tolerance factorable varieties
Let
Lat denote the variety of lattices. In 1982, the second author proved thatLat is strongly tolerance factorable , that is, the members ofLat have... -
Varieties generated by modes of submodes
In a natural way, we can “lift” any operation defined on a set A to an operation on the set of all non-empty subsets of A and obtain from any algebra...
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A mathematical view on the decoupled sites representation
The decoupled sites representation (DSR) is a theoretical instrument which allows to regard complex pH titration curves of biomolecules with several...
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On some congruences of power algebras
In a natural way we can “lift” any operation defined on a set A to an operation on the set of all non-empty subsets of A and obtain from any algebra (
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What is a Finitely Related Object, Categorically?
The concept of a finitely related algebra, as opposed to the ones of finitely presentable and finitely generated ones, is not preserved under...
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Directoid groups
We continue the study of directoid groups, directed abelian groups equipped with an extra binary operation which assigns an upper bound to each...
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A second note on the equational theory of modular ortholattices
We show how to alter the material in [4] to prove that every variety of modular ortholattices is generated by its simple members.
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Terms which are Mal’cev modulo some functions
We derive consequences from the existence of a term which satisfies Mal’cev identities (characterizing permutability) modulo two functions F and G ...
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Endomorphisms of monadic Boolean algebras
A classical result about Boolean algebras independently proved by Magill [10], Maxson [11], and Schein [17] says that non-trivial Boolean algebras...
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Finitary set endofunctors are alg-universal
A category is said to be alg-universal , if every category of universal algebras can be fully embedded into it. We prove here that the category of...