Finitely Generated Varieties of Commutative BCK-algebras: Covers
V\'aclav Cenker
TL;DR
This paper characterizes all covers of finitely generated varieties of commutative BCK-algebras, providing a comprehensive description of their structure and subalgebra relationships.
Contribution
It introduces a construction method to determine all covers of finitely generated cBCK-algebra varieties, expanding understanding of their algebraic hierarchy.
Findings
Subdirectly irreducible cBCK-algebras are rooted trees.
All subdirectly irreducible members are subalgebras of generators.
A new construction method for covers of finitely generated varieties.
Abstract
The article aims at describing all covers of any finitely generated variety of cBCK-algebras. It is known that subdirectly irreducible cBCK-algebras are rooted trees (concerning their order). Also, all subdirectly irreducible members of finitely generated variety are subalgebras of subdirectly irreducible generators of that variety. The first part of the article focuses on subalgebras of finite subdirectly irreducible cBCK-algebras. In the second part of the article, a construction is presented that provides all the covers of any finitely generated variety.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Logic · Rings, Modules, and Algebras · Logic, Reasoning, and Knowledge