आइसोमॉर्फिक 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.

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).

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.

Actually, it is possible to use the Poincaré–Birkhoff–Witt theorem to show that the underlying vector space of W_\lambda is isomorphic to.

This assertion follows from the earlier claim that the Verma module is isomorphic as a vector space to U(\mathfrak{g}_-), along with the Poincaré–Birkhoff–Witt theorem for U(\mathfrak{g}_-).

Instead, he considered the set of isomorphism classes of well-ordered subsets of X and the relation in which the class of A precedes that of B if A is isomorphic with a proper initial segment of B.

Thus E(n) is a direct product of the orthogonal group O(n) and the subgroup of translations T, and O(n) is isomorphic with the quotient group of E(n) by T:.

Additionally, Dih2n has two normal subgroups isomorphic with Dihn.