\(
\newcommand{\cat}[1] {\mathrm{#1}}
\newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})}
\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
\newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}}
\newcommand{\betaReduction}[0] {\rightarrow_{\beta}}
\newcommand{\betaEq}[0] {=_{\beta}}
\newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}}
\newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}}
\newcommand{\groupMul}[1] { \cdot_{\small{#1}}}
\newcommand{\groupAdd}[1] { +_{\small{#1}}}
\newcommand{\inv}[1] {#1^{-1} }
\newcommand{\bm}[1] { \boldsymbol{#1} }
\require{physics}
\require{ams}
\require{mathtools}
\)
Math and science::Algebra::Aluffi
Rings. Additional structure.
As structure is added to rings, a number of useful concepts are graced with
definitions.
- [What?]: a ring whose multiplicative operation is commutative.
- [What?]: a ring where all nonzero elements have two-sided multiplicative inverses.
- [What?]: a ring whose multiplicative operation is commutative and no nonzero element is a zero divisor.
- [What?]: satisfies both 1) and 2) above.
The zero ring is specifically excluded from being considered to be either [...] or [...], despite otherwise meeting the
requirements.
