अंतकृत् इसके अंग्रेजी अर्थ का उदाहरण

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}.

In endomorphism rings .

This concept finds applications especially in the study of endomorphism rings where we have A"nbsp;"nbsp;B.

It states that the space GL(H) of invertible bounded endomorphisms of H is such that all maps from any finite complex Y to GL(H) are [to a constant, for the Neal Morse is the first solo rock album by Neal Morse.

Brazilian models of German descent In algebraic geometry, supersingular elliptic curves form a certain class of elliptic curves over a field of characteristic p"nbsp;>"nbsp;0 with unusually large endomorphism rings.

discovered supersingular elliptic curves during his work on the Riemann hypothesis for elliptic curves by observing that positive characteristic elliptic curves could have endomorphism rings of unusually large rank 4, and developed their basic theory.

The complex elliptic curves with complex multiplication are those for which the endomorphism ring has the maximal possible rank 2.

In positive characteristic it is possible for the endomorphism ring to be even larger: it can be an order in a quaternion algebra of dimension 4, in which case the elliptic curve is supersingular.

Supersingular elliptic curves have many endomorphisms over the algebraic closure \overline{K} in the sense that an elliptic curve is supersingular if and only if its endomorphism algebra (over \overline{K}) is an order in a quaternion algebra.

Thus, their endomorphism algebra (over \overline{K}) has rank 4, while the endomorphism group of every other elliptic curve has only rank 1 or"nbsp;2.

The endomorphism ring of a supersingular elliptic curve can have rank less than 4, and it may be necessary to take a finite extension of the base field K to make the rank of the endomorphism ring 4.

In particular the endomorphism ring of an elliptic curve over a field of prime order is never of rank 4, even if the elliptic curve is supersingular.

If the field K is a finite field of order q, then an elliptic curve over K is supersingular if and only if the trace of the q-power Frobenius endomorphism is congruent to zero modulo p.