Meadows -- algebraic structures with three or more binary operations
type: Item
instance of: scholarly article
title: Meadows -- algebraic structures with three or more binary operations
zbMATH Open document ID: 0813.08003
author: Robert Haas
published in: Journal of Algebra
publication date: 1994-09-27T00:00:00Z
review text: The purpose of this paper is to explore algebraic structures with more than just two linked operations (binary operations). These are produced in the paper by simply adding further sequentially distributive operations to existing rings or fields; the resulting structures are termed meadows. A third operation can be added to a finite field, and occasionally a fourth. Section 1 gives the complete construction and classification of finite meadows. Section 2 presents some three-operation meadows over the integers and the rational numbers, and Section 3 describes a meadow with an infinite set of sequentially distributive operations, generated by ordinary addition and multiplication, over the real numbers. Section 4 demonstrates the essential uniqueness of the latter structure, and Section 5 contains some remarks concerning the significance of the new binary operations, including possible relations to bifurcation theory and chemical kinetics.
Mathematics Subject Classification ID: 08A62
Mathematics Subject Classification ID: 17A99
Mathematics Subject Classification ID: 08A65
zbMATH DE Number: 645080
zbMATH Keywords: binary operations
zbMATH Keywords: meadows
zbMATH Keywords: sequentially distributive operations
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
full work available at URL: jabr.1994.1230
OpenAlex ID: W1996601861
DOI: 10.1006/JABR.1994.1230
Recommended article: Q4869378
Recommended article: Q4332376
Recommended article: The structure of finite meadows
Recommended article: Q4322743
Recommended article: Ternary mappings of triangular algebras
Recommended article: The multiplier algebra of a ternary algebra
Recommended article: Q3507841
Recommended article: Q5690057
Recommended article: The structure of solid binary algebras
description: scientific article; zbMATH DE number 645080