Semigroups with finitely generated universal left congruence
Semigroups with finitely generated universal left congruence
复制标题
具有有限生成的全左同余的半群
DOI：
10.1007/s00605-019-01274-w
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Rida
中科院分区：
文献类型：
--
作者：
Yang Dandan;V. Gould;T. Quinn;Rida
我们考虑半群使得泛左同余$$\omega ^{\ell }$$ω是n-生成的。当然，一个左诺特半群，也就是说，其中所有的左同余是双生成的，满足我们的条件。在幺半群的情况下，$$\omega ^{\ell }$$ω是双生成的条件等价于一些预先存在的概念。特别地，当$$\omega ^{\ell }$$ω生成时，么半群满足左-$${\text {FP}}_1$$FP1型同调有限性条件，我们的研究使我们能够对那些使得$$\omega ^{\ell}$$ω生成的半群进行分类，这些半群属于某些重要的类，如半群的强半格，逆半群，Rees矩阵半群（半群上）与完全正则半群。本文研究了一类使$$\omega ^{\ell }$$ω生成的半群的闭包性质，包括在态象下、直积、半直积、自由积和0-直并.我们的工作受到了更强的条件的启发，在白色的工作中为幺半群陈述了伪有限的条件。在适当的情况下，我们专门研究伪有限半群和幺半群。特别是，我们回答了一个问题，戴尔斯和白色有关性质的伪有限幺半群。
We consider semigroups such that the universal left congruence $$\omega ^{\ell }$$ωℓ is finitely generated. Certainly a left noetherian semigroup, that is, one in which all left congruences are finitely generated, satisfies our condition. In the case of a monoid the condition that $$\omega ^{\ell }$$ωℓ is finitely generated is equivalent to a number of pre-existing notions. In particular, a monoid satisfies the homological finiteness condition of being of type left-$${\text {FP}}_1$$FP1 exactly when $$\omega ^{\ell }$$ωℓ is finitely generated.Our investigations enable us to classify those semigroups such that $$\omega ^{\ell }$$ωℓ is finitely generated that lie in certain important classes, such as strong semilattices of semigroups, inverse semigroups, Rees matrix semigroups (over semigroups) and completely regular semigroups. We consider closure properties for the class of semigroups such that $$\omega ^{\ell }$$ωℓ is finitely generated, including under morphic image, direct product, semi-direct product, free product and 0-direct union. Our work was inspired by the stronger condition, stated for monoids in the work of White, of being pseudo-finite. Where appropriate, we specialise our investigations to pseudo-finite semigroups and monoids. In particular, we answer a question of Dales and White concerning the nature of pseudo-finite monoids.
影响因子：
0.8
作者：
Miller C
通讯作者：
Miller C
影响因子：
0.8
作者：
Gray R
通讯作者：
Gray R