# Opposite ring

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2010 Mathematics Subject Classification: Primary: 16-XX [MSN][ZBL]

of a ring $R$

The ring $R^{\mathrm{op}}$ having the same additive group as $R$ but with multiplication $\circ$ defined by $x \circ y = y \cdot x$ where $\cdot$ is multiplication in $R$.

#### References

• Igor R. Shafarevich, tr. M. Reid, Basic Notions of Algebra, Springer (2006) ISBN 3-540-26474-4. p.67
How to Cite This Entry:
Opposite algebra. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Opposite_algebra&oldid=35161