आइसोमॉर्फ इसके अंग्रेजी अर्थ का उदाहरण

J(n,k) is isomorphic to J(n,n-k).

There is a distance-transitive subgroup of \operatorname{Aut}(J(n,k)) isomorphic to \operatorname{Sym}(n).

As algebras A and \mathcal{G}(A) are distinct (with the exception of the trivial case that A is graded) but as vector spaces they are isomorphic.

The scheme X is determined up to isomorphism by the functor S ↦ X(S); this is the philosophy of identifying a scheme with its functor of points.

Every smooth projective curve X of genus zero over a field k is isomorphic to a conic (degree 2) curve in P2.

If X has a k-rational point, then it is isomorphic to P1 over k, and so its k-rational points are completely understood.

H^{2n}(X) is isomorphic to K (the so-called orientation map).

There is a canonical Künneth isomorphism.

satisfying certain compatibility conditions with respect to functoriality of H and the Künneth isomorphism.

are isomorphisms for i \leqslant n-2 and injections for i \leqslant n-1.

is an isomorphism for i 1, .

It is isomorphic with the Lie algebra of the group of translations and rotations in the plane.

He then showed that every semisimple algebra finite-dimensional can be constructed as a direct sum of simple algebras and that every simple algebra is isomorphic to a matrix algebra for some division ring.