About: Unit (ring theory)

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Unit (ring theory) Goto Sponge NotDistinct Permalink

An Entity of Type : dbo:Person, within Data Space : el.dbpedia.org associated with source document(s)

In algebra, a unit of a ring is an invertible element for the multiplication of the ring. That is, an element u of a ring R is a unit if there exists v in R such that , where 1 is the multiplicative identity; the element v is unique for this property and is called the multiplicative inverse of u. The set of units of R forms a group R× under multiplication, called the group of units or unit group of R. Other notations for the unit group are R∗, U(R), and E(R) (from the German term Einheit).

Attributes	Values
rdf:type	Thing person
rdfs:label	Unit (ring theory) (en)
rdfs:comment	In algebra, a unit of a ring is an invertible element for the multiplication of the ring. That is, an element u of a ring R is a unit if there exists v in R such that , where 1 is the multiplicative identity; the element v is unique for this property and is called the multiplicative inverse of u. The set of units of R forms a group R× under multiplication, called the group of units or unit group of R. Other notations for the unit group are R∗, U(R), and E(R) (from the German term Einheit). (en)
differentFrom	Ring (mathematics)
sameAs	Unit (ring theory)
dbp:wikiPageUsesTemplate	dbt:Anchor dbt:Citation dbt:Cite_book dbt:Distinguish dbt:Efn dbt:Math dbt:Mvar dbt:Notelist dbt:Refbegin dbt:Refend dbt:Reflist dbt:Sfn dbt:Short_description dbt:Sqrt dbt:Sup dbt:Visible_anchor dbt:Void
Subject	1 (number) Algebraic number theory Ring theory Group theory Algebraic properties of elements
gold:hypernym	Identity
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Unit_(ring_theory)?oldid=1062861020&ns=0
Wikipage page ID	289666 (xsd:integer)
page length (characters) of wiki page	10787 (xsd:nonNegativeInteger)
Wikipage revision ID	1062861020 (xsd:integer)
has abstract	In algebra, a unit of a ring is an invertible element for the multiplication of the ring. That is, an element u of a ring R is a unit if there exists v in R such that , where 1 is the multiplicative identity; the element v is unique for this property and is called the multiplicative inverse of u. The set of units of R forms a group R× under multiplication, called the group of units or unit group of R. Other notations for the unit group are R∗, U(R), and E(R) (from the German term Einheit). Less commonly, the term unit is sometimes used to refer to the element 1 of the ring, in expressions like ring with a unit or unit ring, and also unit matrix. Because of this ambiguity, 1 is more commonly called the "unity" or the "identity" of the ring, and the phrases "ring with unity" or a "ring with identity" are used for emphasizing that one consider a ring rather than a rng. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Unit_(ring_theory)
is Wikipage redirect of	Group of units Invertible element Unit (abstract algebra) Unit (algebra) Unit (mathematics) Unit element Unit group
is Link from a Wikipage to another Wikipage of	Green's relations Group (mathematics) Local ring Localization (commutative algebra) Localization of a category Nagao's theorem Noncommutative ring 1 24-cell Abelian group Additive group Adjoint functors Adjugate matrix Algebra homomorphism Algebra over a field Algebraic K-theory Algebraic integer Algebraic number field Algebraic number theory Alternating multilinear map Alternative algebra Artin–Verdier duality Asterisk Atomic domain Automorphism Automorphism group B-admissible representation Banach algebra Berezinian Bilinear form Binary tetrahedral group Biquaternion Cancellation property Carmichael function Cartan–Brauer–Hua theorem Category of rings Free abelian group General linear group Generalized permutation matrix Generating set of a group Glossary of ring theory Dirichlet's unit theorem Dirichlet convolution Discrete Morse theory Discrete valuation ring Divisibility (ring theory) Division (mathematics) Divisor Dual number Dual quaternion Lemniscate elliptic functions Length of a module Mersenne prime Character (mathematics) Clean ring Cubic reciprocity Cyclic group Cyclotomic field

Faceted Search & Find service v1.17_git151 as of Feb 20 2025

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Nov 11 2024, on Linux (x86_64-ubuntu_focal-linux-gnu), Single-Server Edition (72 GB total memory, 1 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software