Category:Isomorphism Preserves Inverses
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This category contains pages concerning Isomorphism Preserves Inverses:
Let $\struct {S, \circ}$ and $\struct {T, *}$ be algebraic structures.
Let $\phi: \struct {S, \circ} \to \struct {T, *}$ be an isomorphism.
Let $\struct {S, \circ}$ have an identity $e_S$.
Then $x^{-1}$ is an inverse of $x$ for $\circ$ if and only if $\map \phi {x^{-1} }$ is an inverse of $\map \phi x$ for $*$.
That is, if and only if:
- $\map \phi {x^{-1} } = \paren {\map \phi x}^{-1}$
Pages in category "Isomorphism Preserves Inverses"
The following 3 pages are in this category, out of 3 total.