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bn:03843949n
Noun Concept
Categories: Algebraic structures, Commutative algebra, Ring theory
EN
integral element  absolute integral closure  complete integral closure  integral  integral closure
EN
In commutative algebra, an element b of a commutative ring B is said to be integral over A, a subring of B, if there are n ≥ 1 and aj in A such that b n + a n − 1 b n − 1 + ⋯ + a 1 b + a 0 = 0. Wikipedia
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EN
In commutative algebra, an element b of a commutative ring B is said to be integral over A, a subring of B, if there are n ≥ 1 and aj in A such that b n + a n − 1 b n − 1 + ⋯ + a 1 b + a 0 = 0. Wikipedia
Given a commutative unital ring R with extension ring S (i.e., that is a subring of S), any element s ∈ S that is a root of some monic polynomial with coefficients in R. Wiktionary
Element of a given ring that is a root of some monic polynomial with coefficients in a given subring. Wiktionary (translation)
IS A
element
DIFFERENT FROM
algebraic element
STUDIED BY
category theory
Wikipedia
EN
integral element
Wikidata
EN
integral element
Wiktionary
EN
integral element
Wikipedia Redirections
EN
absolute integral closure, complete integral closure, integral (ring theory), integral closure, Integral dependence, integral extension, Integral extension of a ring, integral over, integrality

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