Premium
Topological Nearrings on the Euclidean Plane
Author(s) -
MAGILL K. D.
Publication year - 1995
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1995.tb55901.x
Subject(s) - mathematics , multiplication (music) , topological group , constant (computer programming) , group (periodic table) , topology (electrical circuits) , automorphism , euclidean geometry , function (biology) , distributive property , associative property , zero (linguistics) , topological ring , binary number , pure mathematics , topological space , combinatorics , topological vector space , arithmetic , computer science , physics , geometry , quantum mechanics , linguistics , philosophy , evolutionary biology , biology , programming language
Every continuous binary operation* which is right distributive over (R 2 , +), the two‐dimensional topological Euclidean group, is induced by four continuous functions from R 2 to the reals, R. We choose two of these functions to map everything onto zero, we let one be an arbitrary constant function and we let the remaining function be arbitrary. We then find necessary and sufficient conditions on the constant function and the remaining function so that the induced multiplication is associative and, hence, (R 2 , +, *) is a topological nearring. This allows us to completely describe all the induced multiplications which result in topological nearrings with additive group (R 2 , +). In addition, we determine the ideals of each of these nearrings as well as its automorphism group.