# Opposite ring

From Encyclopedia of Mathematics

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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 ring.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Opposite_ring&oldid=35150