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Distributive and Lower-Modular Elements of the Lattice of Monoid Varieties
In the lattice of semigroup varieties, the set of all neutral elements is finite, the set of all distributive elements is countably infinite, and the...
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Canonical extensions, free completely distributive lattices, and complete retracts
We provide a simple proof of a recent result of Morton and van Alten that the canonical extension of a bounded distributive lattice is its free...
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Varieties of aperiodic monoids with central idempotents whose subvariety lattice is distributive
We completely classify all varieties of aperiodic monoids with central idempotents whose subvariety lattice is distributive.
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Representing Distributive Dually Algebraic Lattices
We show that every distributive dually algebraic lattice can be represented as Sp(S, H) with S an algebraic lattice and H a monoid of operators. As a...
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Subordinations on Bounded Distributive Lattices
In this paper we shall study some classes of bounded distributive lattices endowed with a subordination relation, called subordination lattices. We...
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Completely Prime Ideals in Multiplicatively Idempotent Semirings
AbstractStructure properties of multiplicatively idempotent semirings are considered. Basic results concerning completely prime ideals in...
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Sufficient conditions for the finiteness of the 3-generated lattice with modular and distributive type elements among generators
We investigate the finiteness and the infiniteness of the free 3-generated lattice with modular and distributive type elements among generators. For...
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Pointed Lattice Subreducts of Varieties of Residuated Lattices
We study the pointed lattice subreducts of varieties of residuated lattices (RLs) and commutative residuated lattices (CRLs), i.e. lattice subreducts...
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The lattice of varieties of monoids
We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number...
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Pointless Parts of Completely Regular Frames
(Completely regular) locales generalize (Tychonoff) spaces; indeed, the passage from a locale to its spatial sublocale is a well understood...
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Duality for normal lattice expansions and sorted residuated frames with relations
We revisit the problem of Stone duality for lattices with quasioperators, presenting a fresh duality result. The new result is an improvement over...
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Cancellable elements of the lattice of monoid varieties
The set of all cancellable elements of the lattice of semigroup varieties has recently been shown to be countably infinite. But the description of...
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The structure of completely meet irreducible congruences in strongly Fregean algebras
A strongly Fregean algebra is an algebra such that the class of its homomorphic images is Fregean and the variety generated by this algebra is...
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On Convex Directed Subgroups of Pseudo Lattice-Ordered Groups
We show that all convex directed subgroups of a pl -group form a distributive lattice under inclusions that is a Brouwer lattice. We succeeded in...
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General Mixed Lattices
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice...