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| Title of object: |
division ring |
| Canonical Name: |
DivisionRing |
| Type: |
Definition |
| Created on: |
2001-10-19 00:30:52 |
| Modified on: |
2002-07-23 18:07:22 |
| Classification: |
msc:16K99 |
| Synonyms: |
division ring=skew field |
Revision comment (for changes between this and next version):
| Changes for correction #8251 ('link is wrong'). |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic} |
Content:
A {\em division ring} is a ring $D$ with identity such that
\begin{itemize}
\item $1 \neq 0$
\item For all nonzero $a \in D$, there exists $b \in D$ with $a \cdot b = b \cdot a = 1$
\end{itemize}
A field is equivalent to a commutative division ring. |
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