（有界）积分剩余格的射影性
Projectivity in (bounded) integral residuated lattices
摘要：
本文从代数（而不是范畴）的角度研究了各种（有界）交换积分剩余格中的投射代数。特别地，我们在剩余格中使用了一个公认的构造：序数和。它与整除性的相互作用使我们的结果在可除交换积分剩余格的各种类型中有更好的适用范围，并且它允许我们证明许多这样的类型具有每个可除表示代数都是投射的性质.特别是，我们得到的结果（斯通）海廷代数，某些品种的箍，和产品代数。此外，我们研究品种的布尔收缩项，例如，在各种布尔收缩项的所有有限布尔代数是投射。最后，我们把我们的结果与统一理论联系起来。
英文摘要：
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.
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