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Expansions of finite algebras and their congruence lattices
In this paper, we present a novel approach to the construction of new finite algebras and describe the congruence lattices of these algebras. Given a...
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Prime ideals in 0-distributive posets
In the first section of this paper, we prove an analogue of Stone’s Theorem for posets satisfying DCC by using semiprime ideals. We also prove the...
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Remarks on annihilators preserving congruence relations
In this note we shall give some results on annihilators preserving congruence relations, or AP-congruences, in bounded distributive lattices. We...
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Lattice tolerances and congruences
We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.
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The least regular order with respect to a regular congruence on ordered Γ-semigroups
The motivation mainly comes from the conditions of congruences to be regular that are of importance and interest in ordered semigroups. In 1981, Sen...
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Ideals in distributive posets
We prove that any ideal in a distributive (relative to a certain completion) poset is an intersection of prime ideals. Besides that, we give a...
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On the algorithmic construction of the 1960 sectional complement
In 1960, G. Grätzer and E. T. Schmidt proved that every finite distributive lattice can be represented as the congruence lattice of a sectionally...
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Maximality on fuzzy filters of lattices
In this work, we consider a mimetic definition of maximality for fuzzy filters of lattices, and look for some characterization of this definition. We...
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Finite distributive lattices are congruence lattices of almost-geometric lattices
A semimodular lattice L of finite length will be called an almost-geometric lattice if the order J ( L ) of its nonzero join-irreducible elements is a...
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On n-normal posets
A poset Q is called n -normal, if its every prime ideal contains at most n minimal prime ideals. In this paper, using the prime ideal theorem for...
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Coloring of lattices
The concept of coloring is studied for graphs derived from lattices with 0. It is shown that, if such a graph is derived from an atomic or...
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Notes on planar semimodular lattices. IV. The size of a minimal congruence lattice representation with rectangular lattices
Let D be a finite distributive lattice with n join-irreducible elements. In Part III, we proved that D can be represented as the congruence lattice...
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A glimpse of deductive systems in algebra
The concept of a deductive system has been intensively studied in algebraic logic, per se and in connection with various types of filters. In this...
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A natural equivalence for the category of coherent frames
The functor on the category of bounded lattices induced by reversing their order, gives rise to a natural equivalence of coherent frames. We...
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Central elements in pseudoeffect algebras
We introduce the definition of pseudoorthoalgebras and discuss some relationships between orthomodular lattices and pseudoorthoalgebras. Then we...
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Congruences on balanced pseudocomplemented Ockham algebras
The variety bpO consists of those algebras ( L ; ∧ , ∨ , f ,*) of type 〈2, 2, 1, 1, 0, 0〉 where ( L ; ∧ , ∨ , f , 0, 1) is an Ockham algebra, ( L ; ∧ , ∨ , *, 0,...
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Iterative separation in distributive congruence lattices
In [PLOŠČICA, M.: Separation in distributive congruence lattices , Algebra Universalis 49 (2003), 1–12] we defined separable sets in algebraic...
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Weakly representable relation algebras form a variety
We prove that the class of weakly representable relation algebras is closed under homomorphic images, hence it is a variety. As a corollary we...
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The Patch Construction is Dual to Algebraic DCPO Representation
Using the parallel between the preframe and the suplattice approach to locale theory it is shown that the patch construction, as an action on...