论文标题
扭曲产品和伪界posets的残留摘要
Residuation in twist products and pseudo-Kleene posets Abstract
论文作者
论文摘要
M. Busaniche，R。Cignoli，C。Tsinakis和A. M. Wille表明，每个残留的晶格都会在其完整的扭曲产品上诱导残留物。对于他们的构建，他们还使用了晶格操作。我们将这个问题推广到不需要晶格排序的左溶液类固醇。因此，对于完整的扭曲产品，我们不能使用相同的结构。我们提出了另一种适当的结构，但是，该结构并不能保留乘法的交换性和关联性。因此，我们介绍了所谓的操作员残留的posets，以获取另一种保留上述特性的结构，但是完整扭曲产品上的操作员的结果不必是元素，而是子集。我们还将这种结构应用于限制扭曲产品，并提供了必要和充分的条件，在这些条件下，我们获得了伪kleene操作员残留的poset。
M. Busaniche, R. Cignoli, C. Tsinakis and A. M. Wille showed that every residuated lattice induces a residuation on its full twist product. For their construction they used also lattice operations. We generalize this problem to left-residuated groupoids which need not be lattice-ordered. Hence, for the full twist product we cannot use the same construction. We present another appropriate construction which, however, does not preserve commutativity and associativity of multiplication. Hence we introduce so-called operator residuated posets to obtain another construction which preserves the mentioned properties, but the results of operators on the full twist product need not be elements, but may be subsets. We apply this construction also to restricted twist products and present necessary and sufficient conditions under which we obtain a pseudo-Kleene operator residuated poset.
