In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector...
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integer factorization algorithms Matrix congruence, an equivalence relation between two matrices Congruence (manifolds), in the theory of smooth manifolds...
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Modular arithmetic (redirect from Congruence arithmetic)
integer k such that a − b = k m. Congruence modulo m is a congruence relation, meaning that it is an equivalence relation that is compatible with the operations...
29 KB (3,602 words) - 18:28, 25 August 2024
structure. In general, congruence relations play the role of kernels of homomorphisms, and the quotient of a structure by a congruence relation can be formed....
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Quotient (universal algebra) (redirect from Congruence lattice)
using a congruence relation. Quotient algebras are also called factor algebras. Here, the congruence relation must be an equivalence relation that is...
10 KB (1,497 words) - 07:09, 29 January 2023
where "T" denotes the matrix transpose. Matrix congruence is an equivalence relation. Matrix congruence arises when considering the effect of change of...
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In number theory, the Eichler–Shimura congruence relation expresses the local L-function of a modular curve at a prime p in terms of the eigenvalues of...
3 KB (275 words) - 18:48, 26 July 2024
(an element of the Euclidean group E(n)) with f(A) = B. Congruence is an equivalence relation. Two conic sections are congruent if their eccentricities...
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whether a homomorphism is injective. In these cases, the kernel is a congruence relation. This article is a survey for some important types of kernels in...
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Equality (mathematics) (redirect from Equality relation)
when one may be moved to coincide with the other, and the equality/congruence relation is the isomorphism classes of isometries between shapes. Similarly...
26 KB (3,533 words) - 15:09, 28 August 2024