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The 17 pages that link to Quotient ring, each with the reason it gives.

• Finite fieldRelated: A finite extension can be represented as polynomials modulo an irreducible polynomial.

• Polynomial ringRelated: Quotienting by polynomial relations produces coordinate rings and other algebraic structures.

• Quotient groupRelated: It generalizes the quotient construction to rings, where ideals replace normal subgroups.

• Prime idealRelated: Factoring out a prime ideal produces a ring without zero divisors.

• Minimal polynomialRelated: The field generated by an algebraic element is represented by a polynomial quotient using its minimal polynomial.

• Commutative ringRelated: Quotienting by an ideal turns its elements into zero and simplifies ring equations.

• Maximal idealRelated: The quotient by a maximal ideal is a field in a commutative ring with identity.

• Ideal (ring theory)Related: Two-sided ideals define the equivalence classes used to form quotient rings.

• IdealRelated: An ideal supplies exactly the equivalence relation needed to form a quotient ring.

• Noetherian ringRelated: Every quotient of a Noetherian ring remains Noetherian.

• Boolean ringRelated: Quotients preserve the equation x² = x, so every quotient remains Boolean.

• Krull's theoremRelated: A maximal ideal is characterized by its quotient ring being a field.

• Standard part functionRelated: The standard-part map can be understood through a quotient of finite hyperreals.