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Zero ring

In ring theory, a branch of mathematics, the zero ring or trivial ring is the unique ring (up to isomorphism) consisting of one element. (Less commonly, the term "zero ring" is used to refer to any rng of square zero, i.e., a rng in which xy = 0 for all x and y. This article refers to the one-element ring.)

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Definition

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Constructions

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Map overview Semantic statistics

Zero ring

Nodes54
Edges53
Triples29
Avg. degree1.96
Density0.037037
Components1

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Zero ring

Top relations

related to Properties · 17
Zero ring → Artinian, Excluding, First, For, If, In, It, Noetherian, Proof, Second, The, The Krull, This, Thus, When, Whether, Z/nZ
is a · 6
Zero ring → empty scheme.The Krull dimension of the zero ring is, terminal object, terminal object in the category of rings.If A is a nonzero ring, unique ring in which the additive identity 0 and multiplicative identity 1 coincide, unique ring of characteristic 1.The only module for the zero ring is the zero module, unit
related to Constructions · 5
Zero ring → A/I, For, If, M0, The
related to Definition · 1
Zero ring → The

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Important terminology

ring zero ideal unit trivial unique element algebra category rings object domain multiplicative commutative field empty theory one one-element terminal

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Zero ringis aterminal object0.90text
Zero ringis aunique ring in which the additive identity 0 and multiplicative identity 1 coincide0.90text
Zero ringis aunit0.90text
Zero ringis aterminal object in the category of rings.If A is a nonzero ring0.90text
Zero ringis aunique ring of characteristic 1.The only module for the zero ring is the zero module0.90text
Zero ringis aempty scheme.The Krull dimension of the zero ring is0.90text
Zero ringrelated to ConstructionsFor0.60section
Zero ringrelated to ConstructionsA/I0.60section
Zero ringrelated to ConstructionsIf0.60section
Zero ringrelated to ConstructionsM00.60section
Zero ringrelated to ConstructionsThe0.60section
Zero ringrelated to DefinitionThe0.60section

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