2022/05/10 by Wesley Fussner, Fussner, Wesley, George Metcalfe +1 · 3 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebraic structures and combinatorial models #FOS: Mathematics #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2205.05148
openalex publication_date 2022/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that under certain conditions, well-studied algebraic properties transfer from the class QRFSI of the relatively finitely subdirectly irreducible members of a quasivariety Q to the whole quasivariety, and, in certain cases, back again. First, we prove that if Q is relatively congruence-distributive, then it has the Q-congruence extension property if and only if QRFSI has this property. We then prove that if Q has the Q-congruence extension property and QRFSI is closed under subalgebras, then Q has a one-sided amalgamation property (equivalently, for Q, the amalgamation property) if and only if QRFSI has this property. We also establish similar results for the transferable injections property and strong amalgamation property. For each property considered, we specialize our results to the case where Q is a variety -- so that QRFSI is the class of finitely subdirectly irreducible members of Q and the Q-congruence extension property is the usual congruence extension property -- and prove that when Q is finitely generated and congruence-distributive, and QRFSI is closed under subalgebras, possession of the property is decidable. Finally, as a case study, we provide a complete description of the subvarieties of a notable variety of BL-algebras that have the amalgamation property.