论文标题
在一类参与换向晶格的类别中合并
Amalgamation in classes of involutive commutative residuated lattices
论文作者
论文摘要
在既不可分开的，不可分割的也不愿意的涉及换向的残留晶格中研究合并。我们证明，完全有序的涉及换向残留的晶格的几个子类使合并性质（AP）失败。其中包括奇数甚至参与的晶格的类别，其AP的失败源于在线性序的异性同构阳性同态同构的线性序列的阿贝尔群体中观察到的相同的基本原因。相反，我们证明了三个天然子类，这些子类包括势力对称，完全有序的，涉及的交换性残留的晶格，尽管它们使强大的合并特性（SAP）失败，但具有AP。这种失败归因于线性有序的阿贝尔组类别中确定的相同基本原因。此外，我们表明，半线性的，同性恋对称的，奇怪的涉及换向晶格，以及由基准对称 - 对称性，甚至涉及换向的残留链产生的品种，满足了可转移的注射特性（提示），AP的增强。最后，确定任何各种半线性涉及的换向残留的晶格，这些晶格包含各种奇数半连续性的固定晶格，使AP失败。
Amalgamation is investigated in classes of involutive commutative residuated lattices that are neither divisible, nor integral, nor idempotent. We demonstrate that several subclasses of totally ordered involutive commutative residuated lattices fail the Amalgamation Property (AP). These include the classes of odd and even involutive lattices, whose failure of the AP stems from the same fundamental cause observed in the class of discrete linearly ordered abelian groups with positive normal homomorphisms. Conversely, we prove that three natural subclasses, consisting of idempotent-symmetric, totally ordered, involutive commutative residuated lattices, possess the AP, although they fail the Strong Amalgamation Property (SAP). This failure is attributable to the same underlying reason identified in the class of linearly ordered abelian groups. Furthermore, we show that the variety of semilinear, idempotent-symmetric, odd involutive commutative residuated lattices, as well as the variety generated by idempotent-symmetric, even involutive commutative residuated chains, satisfy the Transferable Injections Property (TIP), a strengthening of the AP. Finally, it is established that any variety of semilinear involutive commutative residuated lattices containing the variety of odd semilinear commutative residuated lattices fails the AP.
