The minimal number of generators of a finite semigroup
The minimal number of generators of a finite semigroup
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有限半群的最小生成元数
DOI：
10.1007/s00233-013-9521-8
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发表时间：
2013
期刊：
影响因子：
0.7
通讯作者：
R. Gray
中科院分区：
文献类型：
--
作者：
R. Gray
有限半群的秩是生成半群所需的最小元素数。给出了群上任意（不一定是正则）里斯矩阵半群的秩的公式。该公式用结构矩阵的维数以及从结构矩阵中的条目生成的子群获得的结构群的某个子集的相对秩来表示，假设其采用格雷厄姆范式。然后应用该公式来回答有关变换半群的某些自然族的最小生成集的问题。特别地，考虑确定全变换幺半群（和对称逆半群）的子半群的最大秩的问题。
The rank of a finite semigroup is the smallest number of elements required to generate the semigroup. A formula is given for the rank of an arbitrary (not necessarily regular) Rees matrix semigroup over a group. The formula is expressed in terms of the dimensions of the structure matrix, and the relative rank of a certain subset of the structure group obtained from subgroups generated by entries in the structure matrix, which is assumed to be in Graham normal form. This formula is then applied to answer questions about minimal generating sets of certain natural families of transformation semigroups. In particular, the problem of determining the maximum rank of a subsemigroup of the full transformation monoid (and of the symmetric inverse semigroup) is considered.
影响因子：
1
作者：
Nina E. Menezes;M. Quick;C. Roney-Dougal
通讯作者：
Nina E. Menezes;M. Quick;C. Roney-Dougal