Associative Operations on a Three-Element Set

被引：0

作者：

Diego, Fridrik ^{[1
]}

Jondottir, Kristin Halla ^{[1
]}

机构：

[1] Iceland Univ Educ, IS-105 Reykjavik, Iceland

来源：

MATHEMATICS ENTHUSIAST | 2008年 / 5卷 / 2-3期

关键词：

binary operations; associativity; inclusion-exclusion principle; recreational mathematics;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A set with a binary operation is a fundamental concept in algebra and one of the most fundamental properties of a binary operation is associativity. In this paper the authors discuss binary operations on a three-element set and show, by an inclusion-exclusion argument, that exactly 113 operations out of the 19,683 existing operations on the set are associative. Moreover these 113 associative operations are accounted for by means of their operation tables.

引用

页数：12

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