自由单体的广义

IF 0.7 3区数学 Q2 MATHEMATICS

Semigroup Forum Pub Date : 2024-07-12 DOI:10.1007/s00233-024-10450-w

Mark V. Lawson, Alina Vdovina

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引用次数: 0

摘要

我们通过定义 k-monoids 来概括自由单元。它们只不过是 \(C^{*}\)- 代数理论中使用的单顶点高阶图，但放弃了心数要求。1-单体正是自由单体。接下来，我们将进一步推广 k 单体，使自相似群作用产生这种类型的单体。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Generalizations of free monoids

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Generalizations of free monoids

We generalize free monoids by defining k-monoids. These are nothing other than the one-vertex higher-rank graphs used in \(C^{*}\)-algebra theory with the cardinality requirement waived. The 1-monoids are precisely the free monoids. We then take the next step and generalize k-monoids in such a way that self-similar group actions yield monoids of this type.

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来源期刊

Semigroup Forum 数学-数学

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

12 months

期刊介绍： Semigroup Forum is a platform for speedy and efficient transmission of information on current research in semigroup theory. Scope: Algebraic semigroups, topological semigroups, partially ordered semigroups, semigroups of measures and harmonic analysis on semigroups, numerical semigroups, transformation semigroups, semigroups of operators, and applications of semigroup theory to other disciplines such as ring theory, category theory, automata, logic, etc. Languages: English (preferred), French, German, Russian. Survey Articles: Expository, such as a symposium lecture. Of any length. May include original work, but should present the nonspecialist with a reasonably elementary and self-contained account of the fundamental parts of the subject. Research Articles: Will be subject to the usual refereeing procedure. Research Announcements: Description, limited to eight pages, of new results, mostly without proofs, of full length papers appearing elsewhere. The announcement must be accompanied by a copy of the unabridged version. Short Notes: (Maximum 4 pages) Worthy of the readers'' attention, such as new proofs, significant generalizations of known facts, comments on unsolved problems, historical remarks, etc. Research Problems: Unsolved research problems. Announcements: Of conferences, seminars, and symposia on Semigroup Theory. Abstracts and Bibliographical Items: Abstracts in English, limited to one page, of completed work are solicited. Listings of books, papers, and lecture notes previously published elsewhere and, above all, of new papers for which preprints are available are solicited from all authors. Abstracts for Reviewing Journals: Authors are invited to provide with their manuscript informally a one-page abstract of their contribution with key words and phrases and with subject matter classification. This material will be forwarded to Zentralblatt für Mathematik.