Zero object (algebra)
In algebra, the zero object of a given algebraic structure is, in the sense explained below, the simplest object of such structure. As a set it is a singleton, and as a magma has a trivial structure, which is also an abelian group. The aforementioned abelian group structure is usually identified as addition, and the only element is called zero, so the object itself is typically denoted as {0}. One often refers to the trivial object (of a specified category) since every trivial object is isomorphic to any other (under a unique isomorphism). κ0 = 0 , where κ ∈ R.
Additive categoryCartesian monoidal categoryDivision algebraGlossary of representation theoryHilbert's syzygy theoremInitial and terminal objectsIrreducible representationKernel (algebra)Linear relationLinear subspaceMatrix (mathematics)Pseudo-Euclidean spaceReal coordinate spaceRepresentation theoryStone–von Neumann theoremTrivial algebraTrivial groupTrivial moduleZero-dimensional vector spaceZero moduleZero representationZero spaceZero vector space
Link from a Wikipage to another Wikipage
primaryTopic
Zero object (algebra)
In algebra, the zero object of a given algebraic structure is, in the sense explained below, the simplest object of such structure. As a set it is a singleton, and as a magma has a trivial structure, which is also an abelian group. The aforementioned abelian group structure is usually identified as addition, and the only element is called zero, so the object itself is typically denoted as {0}. One often refers to the trivial object (of a specified category) since every trivial object is isomorphic to any other (under a unique isomorphism). κ0 = 0 , where κ ∈ R.
has abstract
In algebra, the zero object of ...... dition, and a trivial module .
@en
Link from a Wikipage to an external page
Wikipage page ID
page length (characters) of wiki page
Wikipage revision ID
953,815,227
Link from a Wikipage to another Wikipage
author
Barile, Margherita
@en
id
TrivialModule
@en
ZeroModule
@en
title
Trivial Module
@en
Zero Module
@en
wikiPageUsesTemplate
comment
In algebra, the zero object of ...... rphism). κ0 = 0 , where κ ∈ R.
@en
label
Zero object (algebra)
@en