论文标题
部分格子的扩展和一致性
Extensions and congruences of partial lattices
论文作者
论文摘要
对于部分晶格l所谓的两点延长是为了扩展到晶格的定义。在这种情况下，广泛用于部分代数的一点点扩展不起作用，即部分晶格的单点扩展不必是晶格，我们的动机是我们的动机。我们描述了这些两点扩展，并证明了它们的几个属性。我们介绍了部分晶格的一致性概念，并展示了其与同态概念及其与相应的两点扩展的一致性的关系。特别地，我们证明，l的一致性e的部分晶格l再次是部分晶格，而L/e的两点扩展是与E的一致性L*生成的L*生成的L*的两点扩展L*的商的同构相同。
For a partial lattice L the so-called two-point extension is defined in order to extend L to a lattice. We are motivated by the fact that the one-point extension broadly used for partial algebras does not work in this case, i.e. the one-point extension of a partial lattice need not be a lattice. We describe these two-point extensions and prove several properties of them. We introduce the concept of a congruence on a partial lattice and show its relationship to the notion of a homomorphism and its connections with congruences on the corresponding two-point extension. In particular we prove that the quotient L/E of a partial lattice L by a congruence E on L is again a partial lattice and that the two-point extension of L/E is isomorphic to the quotient lattice of the two-point extension L* of L by the congruence on L* generated by E. Several illustrative examples are enclosed.
