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Congruence relation

Equivalence relation in algebra

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Record originEnglish Wikipedia
Text licenseCC BY-SA 4.0
Source revisionJul 9, 2026
Entity authoritySource title only
Source-derived summary

In abstract algebra, a congruence relation is an equivalence relation on an algebraic structure that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements. Every congruence relation has a corresponding quotient structure, whose elements are the equivalence classes for the relation.

Editorial summary

The public source identifies “Congruence relation” as equivalence relation in algebra. This brief keeps that definition visible, then builds a research path around Congruence, relation and Equivalence.

Editorial reviewA concise reference frame for defining the subject, testing terminology and identifying the institution closest to the evidence. The current 51-word lead offers orientation but no explicit four-digit date, so chronology should not be assumed. The selected authority fields contribute no independent date. Its value is orientation rather than verdict, with Congruence, relation and Equivalence providing the first useful test.
Editorial analysis

Why this record matters

A short description can identify a subject without explaining its stakes. For “Congruence relation”, the useful work is to connect “equivalence relation in algebra” to the records capable of establishing context and consequence.

Evidence profile

Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Jul 9, 2026.

Critical limits

Overview language is designed for orientation and should not be treated as a substitute for the evidence cited beneath it. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.

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Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.

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Source & attribution

This entry incorporates text from “Congruence relation” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.