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searching for Algebraic integer 8 found (43 total)

alternate case: algebraic integer

Ring class field (219 words) [view diff] exact match in snippet view article find links to article

completely in L if and only if p splits completely in K. L=K(a) for a an algebraic integer with minimal polynomial over Q of degree h(-4n), the class number
Proofs of quadratic reciprocity (3,994 words) [view diff] exact match in snippet view article find links to article
{\textstyle \tau ^{2}=2} . Because τ {\displaystyle \tau } is an algebraic integer, if p is an odd prime it makes sense to talk about it modulo p. (Formally
Lindemann–Weierstrass theorem (4,699 words) [view diff] exact match in snippet view article find links to article
f i ( j ) ( α k ) {\displaystyle f_{i}^{(j)}(\alpha _{k})} is an algebraic integer which is divisible by p! for j ≥ p {\displaystyle j\geq p} and vanishes
Lehmer's conjecture (1,675 words) [view diff] exact match in snippet view article find links to article
algebraic number so m ( P ) {\displaystyle m(P)} is the logarithm of an algebraic integer. It also shows that m ( P ) ≥ 0 {\displaystyle m(P)\geq 0} and that
Baker's theorem (3,372 words) [view diff] exact match in snippet view article find links to article
point are given by algebraic integers times known constants. If an algebraic integer has all its conjugates bounded by a known constant, then it cannot
Mersenne prime (9,421 words) [view diff] exact match in snippet view article find links to article
former is not a prime. This can be remedied by allowing b to be an algebraic integer instead of an integer: In the ring of integers (on real numbers),
Cayley–Hamilton theorem (10,729 words) [view diff] exact match in snippet view article find links to article
_{1},\ldots ,\alpha _{k}]} of Q {\displaystyle \mathbb {Q} } and an algebraic integer α ∈ Q [ α 1 , … , α k ] {\displaystyle \alpha \in \mathbb {Q} [\alpha
Principalization (algebra) (8,949 words) [view diff] exact match in snippet view article
integer if necessary we may assume that A {\displaystyle A} is an algebraic integer. The non-unit A {\displaystyle A} is generator of an ambiguous principal