论文标题
（有限的）积分残留晶格中的投影率
Projectivity in (bounded) integral residuated lattices
论文作者
论文摘要
在本文中，我们研究了来自代数（而不是分类）观点的（有限的）（有限）的（有限）的（有限的）内置残留晶格的投射代数。特别是我们在残留的晶格中使用良好的结构：序数总和。它与分裂性的相互作用使我们的结果在各种分割的交换式固定格子的范围内具有更好的范围，并且它使我们能够证明许多此类品种具有每个有限呈现的代数都投影的特性。特别是，我们在（Stonean）Heyting代数，某些箍和产品代数上获得结果。此外，我们研究了带有布尔回收项的品种，例如，在具有布尔回收项的多种情况下，所有有限的布尔代数都投影了。最后，我们将结果与统一理论联系起来。
In this paper we study projective algebras in varieties of (bounded) commutative integral residuated lattices from an algebraic (as opposed to categorical) point of view. In particular we use a well-established construction in residuated lattices: the ordinal sum. Its interaction with divisibility makes our results have a better scope in varieties of divisibile commutative integral residuated lattices, and it allows us to show that many such varieties have the property that every finitely presented algebra is projective. In particular, we obtain results on (Stonean) Heyting algebras, certain varieties of hoops, and product algebras. Moreover, we study varieties with a Boolean retraction term, showing for instance that in a variety with a Boolean retraction term all finite Boolean algebras are projective. Finally, we connect our results with the theory of Unification.
