On generators and relations for unions of semigroups
On generators and relations for unions of semigroups
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关于半群并集的生成元和关系
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
N. Ruškuc
中科院分区：
文献类型：
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作者：
I. M. Araújo;M. Branco;V. H. Fernandes;G. Gomes;N. Ruškuc
研究了半群的一般并、半群的带、幺半群的带、半群的半格和半群的强半格的有限生成与可表示性。例如，证明了幺半群Sα（α∈ Y）的一个带Y是幺半群生成的当且仅当Y是有限的且所有Sα都是幺半群生成的.作为对比，给出了一个非双表示的双生成半群的例子，它是两个双表示的子半群的不交并。
Finite generation and presentability of general unions of semigroups, as well as of bands of semigroups, bands of monoids, semilattices of semigroups and strong semilattices of semigroups, are investigated. For instance, it is proved that a band Y of monoids Sα (α∈ Y ) is finitely generated/presented if and only if Y is finite and all Sα are finitely generated/presented. By way of contrast, an example is exhibited of a finitely generated semigroup which is not finitely presented, but which is a disjoint union of two finitely presented subsemigroups.