Completion and finite embeddability property for residuated ordered algebras.
Completion and finite embeddability property for residuated ordered algebras.
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DOI：
10.1007/s00012-010-0060-9
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发表时间：
2009-09
影响因子：
0.6
通讯作者：
C. J. Alten
中科院分区：
文献类型：
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作者：
C. J. Alten
一个剩余序代数是一个带有额外“剩余”运算的偏序集合。给出了一种从剩余序代数的任何部分子代数出发，构造该部分子代数嵌入的完全代数的构造方法。给出了当选择有限部分子代数时，所构造的代数是有限的条件。这意味着“有限嵌入性质”为给定类的剩余有序代数。在选择整个代数作为部分子代数的情况下，构造是代数的底层阶的完备化。一个计划的不等式被描述为具有被保存的上述建设的属性。因此，这些保留结果扩展了有限可嵌入性和完备性的结果。
A residuated ordered algebra is a partially ordered set with additional ‘residuated’ operations. A construction is presented that, from any partial subalgebra of a residuated ordered algebra, constructs a complete algebra into which the partial subalgebra embeds. Conditions are given under which the constructed algebra is finite whenever a finite partial subalgebra is chosen. This implies the ‘finite embeddability property’ for the given class of residuated ordered algebras. In the case that the whole algebra is chosen as the partial subalgebra, the construction is a completion of the underlying order of the algebra. A scheme of inequalities is described that are shown to have the property of being preserved by the above construction. These preservation results thus extend the results on the finite embeddability property and completion.