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Characterizations of near-Heyting algebras
A near-Heyting algebra is a join-semilattice with a greatest element such that every principal upset is a Heyting algebra. We will present several...
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Projectivity in (bounded) commutative integral residuated lattices
In this paper, we study projective algebras in varieties of (bounded) commutative integral residuated lattices. We make use of a well-established...
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Right-cancellable protomodular algebras
A new protomodular analog of the classical criterion for the existence of a group term in the algebraic theory of a variety of universal algebras is...
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Weakly Schreier extensions for general algebras
Weakly Schreier split extensions are a reasonably large, yet well-understood class of monoid extensions, which generalise some aspects of split...
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On a statement of O. Frink about free pseudo-complemented meet-semilattices
Orrin Frink in 1962 stated incorrectly, that there exist free pseudocomplemented meet-semilattices, which are not lattices. This is disproved in the...
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Constructive Semigroups with Apartness: A State of the Art
This chapter aims to provide a clear and understandable picture of constructive semigroups with apartness in Bishop’s style of constructive...
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The existence of states based on Glivenko semihoops
In this paper, we mainly investigate the existence of states based on the Glivenko theorem in bounded semihoops, which are building blocks for the...
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Characterization of Residuated Lattices via Multipliers
In the paper, we introduce some of multipliers on residuated lattices and investigate the relations among them. First, basing on the properties of...
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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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Presenting Quotient Locales
It is often useful to be able to deal with locales in terms of presentations of their underlying frames, or equivalently, the geometric theories...
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An Introduction to Regular Categories
This paper provides a short introduction to the notion of regular category and its use in categorical algebra. We first prove some of its basic...
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Wirkungsgeschichte und Positionen der Forschung
In diesem Kapitel wollen wir die Wirkungsgeschichte von Dedekinds Werk beschreiben und Themen und Fragestellungen aus der heutigen Forschung...