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searching for Zero divisor 17 found (71 total)

Topological divisor of zero (263 words) [view diff] no match in snippet view article find links to article

In mathematics, an element z {\displaystyle z} of a Banach algebra A {\displaystyle A} is called a topological divisor of zero if there exists a sequence

Regular sequence (1,229 words) [view diff] no match in snippet view article find links to article

non-zero-divisor on M if r m = 0 implies m = 0 for m in M. An M-regular sequence is a sequence r1, ..., rd in R such that ri is a not a zero-divisor on

Complete intersection ring (847 words) [view diff] exact match in snippet view article find links to article

greater than 0 and x is an element in the maximal ideal that is not a zero divisor then R is a complete intersection ring if and only if R/(x) is. (If the

Brainfuck (1,780 words) [view diff] exact match in snippet view article find links to article

divisor if quotient was 2 ]<<[<<->>-]>> Zero divisor and subtract 13 from copy if quotient was 1 ]<<[<<+>>-] Zero divisor and add 13 to copy if quotient was

Evdokimov's algorithm (597 words) [view diff] no match in snippet view article find links to article

A=X{\bmod {f}}} ). The main problem here is to find efficiently a nonzero zero-divisor in the algebra. The GRH is used only to take roots in finite fields in

Cohen–Macaulay ring (3,098 words) [view diff] no match in snippet view article find links to article

R[x] and the power series ring R[[x]] are Cohen–Macaulay. For a non-zero-divisor u in the maximal ideal of a Noetherian local ring R, R is Cohen–Macaulay

Combinatorial commutative algebra (539 words) [view diff] no match in snippet view article find links to article

and Claudio Procesi. Algebraic combinatorics Polyhedral combinatorics Zero-divisor graph A foundational paper on Stanley–Reisner complexes by one of the

Divisible group (1,411 words) [view diff] no match in snippet view article find links to article

rM = M for all nonzero r in R. (It is sometimes required that r is not a zero-divisor, and some authors require that R is a domain.) For every principal left

Beauville–Laszlo theorem (1,161 words) [view diff] exact match in snippet view article find links to article

Â; both are A-algebras. In the following we assume that f is a non-zero divisor. Geometrically, A is viewed as a scheme X = Spec A and f as a divisor

Dehornoy order (1,551 words) [view diff] no match in snippet view article find links to article

\mathbb {Z} B_{n}} and C B n {\displaystyle \mathbb {C} B_{n}} have no zero-divisor. For n ⩾ 3 {\displaystyle n\geqslant 3} , the Dehornoy order is not invariant

Serre's criterion for normality (956 words) [view diff] exact match in snippet view article find links to article

than one, then p {\displaystyle {\mathfrak {p}}} would contain a non zero divisor in A / g A {\displaystyle A/gA} . However, p {\displaystyle {\mathfrak

Rng (algebra) (2,210 words) [view diff] no match in snippet view article

homomorphism from a ring to a rng, and the image of f contains a non-zero-divisor of S, then S is a ring, and f is a ring homomorphism. Every rng R can

Divisor (algebraic geometry) (6,609 words) [view diff] exact match in snippet view article

affine subset U = Spec A such that U ∩ D = Spec A / (f), where f is a non-zero divisor in A. The sum of two effective Cartier divisors corresponds to multiplication

Lucien Szpiro (1,182 words) [view diff] exact match in snippet view article find links to article

Szpiro's research in commutative algebra led to his proof of the Auslander zero divisor conjecture. Together with Christian Peskine, he developed the liaison

Dimension theory (algebra) (6,957 words) [view diff] no match in snippet view article

D=R/{\mathfrak {p}}_{0}} and x a nonzero nonunit element in D. Since x is not a zero-divisor, we have the exact sequence 0 → D → x D → D / x D → 0. {\displaystyle

Real hyperelliptic curve (2,654 words) [view diff] exact match in snippet view article find links to article

S=\{\infty _{1},\infty _{2}\}} . The first one is to represent a degree zero divisor by D ¯ {\displaystyle {\bar {D}}} such that D = ∑ i = 1 r P i − r ∞ 2

Hensel's lemma (9,047 words) [view diff] no match in snippet view article find links to article

{\mathfrak {m}}}.} Furthermore, if f ′ ( a ) {\displaystyle f'(a)} is not a zero-divisor then b is unique. This result can be generalized to several variables