Antiassociative magmas

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-11-11 DOI:10.1007/s10231-024-01512-5

Ryszard Mazurek

引用次数: 0

Abstract

A magma S is said to be antiassociative if \((ab)c \ne a(bc)\) holds for any elements a, b, c of S. Antiassociative magmas lie at the opposite pole from associative ones, known as semigroups. In this paper, we study antiassociative magmas focusing on their properties and examples that can be seen from Cayley tables. We provide a test for the antiassociativity of a finite magma and give some general methods for constructing antiassociative magmas. We also characterize, describe, and count all antiassociative magma structures on a 3-element set, all their isomorphism classes, and all classes of equivalent magmas of this type.

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Antiassociative岩浆

如果\((ab)c \ne a(bc)\)对S中的任意元素A、b、c都成立，那么岩浆S就是反结合岩浆，反结合岩浆位于与结合岩浆相反的极，称为半群。本文对反结合岩浆进行了研究，重点讨论了它们的性质和从Cayley表中可以看到的例子。给出了有限岩浆反结合性的检验方法，并给出了构造反结合性岩浆的一般方法。我们还在一个3元集合上对所有反结合岩浆构造进行了表征、描述和计数，并计算了它们的所有同构类，以及这类岩浆的所有等效类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.