Year: 2024
Type: article
Abstract: A map f : R → S {f\colon R\to S} between (associative, unital, but not necessarily commutative) rings is a brachymorphism if f ( 1 + x ) = 1 + f ( x ) {f(1+x)=1+f(x)} and f ( x y ) = f ( x ) f ( y ) {f(xy)=f(x)f(y)} whenever x , y ∈ R {x,y\in R} . We tackle the problem whether every brachymorphism is additive (i.e., f ( x + y ) = f ( x ) + f ( y ) {f(x+y)=f(x)+f(y)} ), showing that in many contexts, including the following, the answer is positive: • R is finite (or, more generally, R is left or right Artinian); • R is any ring of 2 × 2 {2\times 2} matrices over a commutative ring;
Source: Forum Mathematicum
Author: Friedrich Wehrung
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402129071