Difference between revisions of "Anti-isomorphism of rings"
From Encyclopedia of Mathematics
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A mapping $\phi$ of a ring $A$ into a ring $B$ that is an [[Isomorphism|isomorphism]] of the additive group of $A$ onto the additive group of $B$ and for which $(ab)\phi=b\phi\cdot a\phi$ ($a,b\in A$). | A mapping $\phi$ of a ring $A$ into a ring $B$ that is an [[Isomorphism|isomorphism]] of the additive group of $A$ onto the additive group of $B$ and for which $(ab)\phi=b\phi\cdot a\phi$ ($a,b\in A$). | ||
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| + | An ''anti-automorphism'' is an anti-isomorphism of a ring to itself. | ||
Revision as of 21:37, 29 November 2014
A mapping $\phi$ of a ring $A$ into a ring $B$ that is an isomorphism of the additive group of $A$ onto the additive group of $B$ and for which $(ab)\phi=b\phi\cdot a\phi$ ($a,b\in A$).
An anti-automorphism is an anti-isomorphism of a ring to itself.
How to Cite This Entry:
Anti-isomorphism of rings. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Anti-isomorphism_of_rings&oldid=35143
Anti-isomorphism of rings. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Anti-isomorphism_of_rings&oldid=35143
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article