Commutative regular rings

Abbreviation: CRRng

Definition

A commutative regular ring is a regular rings $\mathbf{R}=\langle R,+,-,0,\cdot,1 \rangle$ such that $\cdot$ is commutative: $x\cdot y=y\cdot x$

Morphisms

Let $\mathbf{R}$ and $\mathbf{S}$ be commutative regular rings. A morphism from $\mathbf{R}$ to $\mathbf{S}$ is a function $h:R\rightarrow S$ that is a homomorphism:

$h(x+y)=h(x)+h(y)$, $h(x\cdot y)=h(x)\cdot h(y)$, $h(1)=1$

Examples

Example 1:

Basic results

Properties

Finite members

$\begin{array}{lr} f(1)= &1\\ f(2)= &\\ f(3)= &\\ f(4)= &\\ f(5)= &\\ f(6)= &\\ \end{array}$

Subclasses

Superclasses

References