अरूपता इसके अंग्रेजी अर्थ का उदाहरण

Homomorphisms in the Service of Geometry, by Sherman K.

Automorphism group .

The species, first identified in 1850, exhibits diurnal behaviour and marked sexual dimorphism.

This means that a morphism of schemes f: X → Spec(k) is given.

Then a k-point of X means a section of this morphism, that is, a morphism a: Spec(k) → X such that the composition fa is the identity on Spec(k).

More generally, for a scheme X over a commutative ring R and any commutative R-algebra S, the set X(S) of S-points of X means the set of morphisms Spec(S) → X over Spec(R).

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.

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, .

The anthropomorphism and metaphorical embodiment of gross social forces is common in Grass's work; here the sentence "It was a young cat, but no kitten" describes the German state in the 1940s — young but by no means innocent (p.

Lie's Theorem states that if V is a finite-dimensional vector space over an algebraically closed field of characteristic zero, and \mathfrak{g} is a solvable Lie algebra, and if \pi is a representation of \mathfrak{g} over V, then there exists a simultaneous eigenvector v \in V of the endomorphisms \pi(X) for all elements X \in \mathfrak{g}.