论文标题
转移定理以有限的细分不可约定代数
Transfer theorems for finitely subdirectly irreducible algebras
论文作者
论文摘要
我们表明，在某些条件下，经过深入研究的代数属性从类$ \ Mathcal {q} _ {_ \ \ text {rfsi}} $的相对有限的Quasivarietio $ $ \ Mathcal {Q} $ for Pasesivarion和某些case ers，Refly and Lever，以及某些情况下，再一次，以及，再一次，再加上，，再加上一定的case，又有一定的case，又一次。首先，我们证明，如果$ \ Mathcal {q} $相对一致，那么它具有$ \ MATHCAL {q} $ - 同时扩展属性，并且仅当$ \ Mathcal {q} _ {_ {_ \ _ \ text {_ \ text {rfsi}} $时才具有此属性。然后，我们证明，如果$ \ Mathcal {q} $具有$ \ Mathcal {Q} $ - 一致性扩展属性和$ \ Mathcal {q} _ {_ \ _ \ text {rfsi}} $在subalgebras下关闭，则是$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ mathgam propertect（ $ \ MATHCAL {Q} $，AMALGAMATION属性）时，仅当$ \ Mathcal {q} _ {_ \ text {rfsi}} $具有此属性。我们还为可转移的注射属性和强大的合并性能建立了相似的结果。对于考虑的每个属性，我们将结果专门针对$ \ Mathcal {q} $是一个多样性的情况 - 因此，$ \ \ \ \ \ \ \ \ \ \ \ \ {_ {_ \ text {rfsi}} $是有限的属于$ \ mathcal的$ \ mathcal {qu} $的$ \ \ \ mather的$ {q \ qu {一致性扩展属性 - 证明，当$ \ Mathcal {q} $有限生成并一致地分发时，$ \ Mathcal {q} _ {_ \ text {rfsi}} $在子代理下关闭，该物业的拥有。最后，作为一个案例研究，我们提供了具有合并性质的众多BL-Elgebras的次视角的完整描述。
We show that under certain conditions, well-studied algebraic properties transfer from the class $\mathcal{Q}_{_\text{RFSI}}$ of the relatively finitely subdirectly irreducible members of a quasivariety $\mathcal{Q}$ to the whole quasivariety, and, in certain cases, back again. First, we prove that if $\mathcal{Q}$ is relatively congruence-distributive, then it has the $\mathcal{Q}$-congruence extension property if and only if $\mathcal{Q}_{_\text{RFSI}}$ has this property. We then prove that if $\mathcal{Q}$ has the $\mathcal{Q}$-congruence extension property and $\mathcal{Q}_{_\text{RFSI}}$ is closed under subalgebras, then $\mathcal{Q}$ has a one-sided amalgamation property (equivalently, for $\mathcal{Q}$, the amalgamation property) if and only if $\mathcal{Q}_{_\text{RFSI}}$ 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 $\mathcal{Q}$ is a variety -- so that $\mathcal{Q}_{_\text{RFSI}}$ is the class of finitely subdirectly irreducible members of $\mathcal{Q}$ and the $\mathcal{Q}$-congruence extension property is the usual congruence extension property -- and prove that when $\mathcal{Q}$ is finitely generated and congruence-distributive, and $\mathcal{Q}_{_\text{RFSI}}$ 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.
