Categories and General Algebraic Structures with Applications

Categories and General Algebraic Structures with Applications

Some categorical and algebraic results on (distributive) nearlattices

Document Type : Research Paper

Author
Universidad Nacional de La Pampa, Facultad de Ciencias Exactas, Naturales, Santa Rosa, Argentina
10.48308/cgasa.2026.245149.1641
Abstract
The goal of this article is to determine whether the varieties of $N$-algebras (nearlattices) and $DN$-algebras (distributive nearlattices) satisfy certain categorical and algebraic properties. Specifically, we provide a characterization of the free $DN$-algebra freely generated by a finite set, and establish a connection between free $DN$-algebras and the free distributive lattice extensions of $DN$-algebras. We also prove that the variety of $DN$-algebras satisfies the amalgamation property but fails to satisfy the strong amalgamation property, whereas the category of $N$-algebras does not possess the amalgamation property. Finally, we show that, in the algebraic categories of $N$-algebras and $DN$-algebras, not every epimorphism is surjective.
Keywords
Subjects

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Articles in Press, Accepted Manuscript
Available Online from 11 September 2026