On Subsemigroups of Finitely Presented Semigroups
On Subsemigroups of Finitely Presented Semigroups
复制标题
关于有限呈现半群的子半群
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
R. Thomas
中科院分区：
文献类型：
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作者：
C. Campbell;E. Robertson;N. Ruškuc;R. Thomas
本文研究了双表示半群的子半群的性质，特别是关于双表示的性质。更准确地说，我们将考虑以下各种情况：主要问题。设S是一个半群. - 是的- 是的i是S的每个子半群理想、单侧理想生成的吗？- 是的- 是的ii是否S的每个子半群理想、单侧理想都是由半群生成的？- 是的- 是的iii是S中每个子半群理想，有限指标的单侧理想.介绍了？指数的定义见下文。例如，如果S是有限的，则所有这些问题都有肯定的答案。- 是的不那么平凡地，如果S是交换半群，则ii有肯定的wx wx答案;见12。在文献[2]中，我们还证明了一个有限指标的双边理想总是有限指标的。
The purpose of this paper is to investigate properties of subsemigroups of finitely presented semigroups, particularly with respect to the property of being finitely presented. More precisely, we will consider various instances of the following: Main Problem. Let S be a finitely presented semigroup. Ž . Ž . i Is every subsemigroup ideal, one-sided ideal of S finitely generated? Ž . Ž . ii Is every subsemigroup ideal, one-sided ideal of S which is finitely generated as a semigroup finitely presented? Ž . Ž . iii Is every subsemigroup ideal, one-sided ideal of finite index in S Ž . finitely presented? For the definition of index see below. For example, if S is finite all these questions have an affirmative answer. Ž . Less trivially, if S is a commutative semigroup then ii has an affirmative w x w x answer; see 12 . Also, in 2 it has been proved that a two-sided ideal of finite index in a finitely presented semigroup is always finitely presented.