Classification of All Associative Mono-n-ary Algebras with 2 Elements
Classification of All Associative Mono-n-ary Algebras with 2 Elements
复制标题
所有结合二元一元代数的分类
DOI：
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发表时间：
2009
影响因子：
1.2
通讯作者：
S. Andres
中科院分区：
文献类型：
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作者：
S. Andres
我们考虑代数与一个单一？-ary运算和某种类型的结合性。我们证明（直到同构）恰好有5个
这些联想单？-ary代数与2元素的偶数？≥ 2和6表示奇数？≥ 3。这些代数被明确地描述。证明了对于至少有4个元素的代数，类似的结果是不可能的。给出了一个关于字符串控制位赋值的应用。
We consider algebras with a single ? -ary operation and a certain type of associativity. We prove that (up to isomorphism) there are exactly 5
of these associative mono- ? -ary algebras with 2 elements for even ? ≥ 2 and 6 for odd ? ≥ 3 . These algebras are described explicitly. It is shown that a similar result is impossible for algebras with at least 4 elements. An application concerning the assignment of a control bit to a string is given.