Abstract Clone Theory
Abstract Clone Theory
复制标题
抽象克隆理论
DOI：
10.1007/978-94-017-0697-1_11
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发表时间：
1993
影响因子：
1
通讯作者：
W. Taylor
中科院分区：
文献类型：
--
作者：
W. Taylor
具体克隆是集合上的一系列操作，包含所有投影操作，并在所有有意义的组合下关闭。这里讨论的抽象克隆形成了具体概念的公理化版本。它们与具体克隆的关系就像群与置换群的关系一样。粗略地说，抽象克隆C的每个表示是一个代数A，所有这些代数A的族是一个簇V。这种对应是克隆C的同构类型和簇V的等价类之间的双射。
A concrete clone is a family of operations on a set, containing all projection operations and closed under all meaningful compositions. The abstract clones discussed here form an axiomatic version of the concrete notion. They stand in the same relation to concrete clones as that of groups to permutation groups. Roughly speaking, each representation of an abstract clone C is an algebra A, and the family of all these algebras A is a variety V. This correspondence is bijective between isomorphism types of clones C and equivalence classes of varieties V. In this context, surjective clone homomorphisms correspond to the embedding of one variety in another, and injective homomorphisms correspond to the formation of reduct varieties.