The variety of complemented lattices where conjunction and implication form an adjoint pair
Year: 2025
Type: article
Abstract: The Sasaki projection was introduced as a mapping from the lattice of closed subspaces of a Hilbert space onto one of its segments. To use this projection and its dual so-called Sasaki operations were introduced by the second two authors in [4] and [6]. In [6] there are described several classes of lattices, $\lambda $-lattices and semirings where the Sasaki operations form an adjoint pair. In the present paper we prove that the class of complemented lattices with this property forms a variety and we explicitly state its defining identities. Moreover, we prove that this variety $\mathcal V$ is congruence permutable and regular. Hence every ideal $I$ of some member $\mathbf L$ of $\mathcal V$ is a kernel of some congruence on $\mathbf L$. Finally, we determine a finite basis of so-called ideal terms and describe the congruence $\varTheta _{I}$ determined by the ideal $I$.
Source: Journal of Logic and Computation
Authors: Václav Cenker, Ivan Chajda, Helmut LÄnger
Institutions: Palacký University Olomouc, TU Wien
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,533
OpenAlex ID: W4409943443