Mobi algebra as an abstraction to the unit interval and its comparison to rings

被引：2

作者：

Fatelo, J. P. ^{[1
]}

Martins-Ferreira, N. ^{[1
]}

机构：

[1] Polytech Inst Leiria, Ctr Rapid & Sustainable Prod Dev CDRSP, Sch Technol & Management, P-2411901 Leiria, Portugal

来源：

COMMUNICATIONS IN ALGEBRA | 2019年 / 47卷 / 03期

关键词：

Mobi algebra; involutive medial monoid; midpoint algebras; unitary rings; unit interval; ternary operation; geodesic path;

D O I：

10.1080/00927872.2018.1501575

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a new algebraic structure, called mobi algebra, consisting of three constants and one ternary operation. The canonical example of a mobi algebra is the unit interval with the three constants 0, 1, and and the ternary operation given by the formula . We study some of its properties and prove that every unitary ring with one half uniquely determines and is uniquely determined by a mobi algebra with one double. Another algebraic structure, called involutive medial monoid (IMM), is considered to establish the passage between rings and mobi algebras.

引用

页码：1197 / 1214

页数：18

共 47 条

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