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Difference between revisions of "User:Richard Pinch/sandbox-14"

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=Generating set=
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'''Generating set''' may refer to
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* For an algebraic object $A$, a set $S$ such that the smallest subobject of $A$ containing $S$ is $A$ itself: a set $S$ such that $A$ consists of all elements resulting from applying the algebraic operations of $A$ to combinations of elements of $S$.
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** A [[spanning set]] for a module over a ring, or a vector space;
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** The set of generators in a [[Presentation|group presentation]].
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* For the special cases of a [[free algebraic system]] on a given set of generators:
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** [[Free algebra]]:
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** [[Free group]];
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** [[Free semi-group]].
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See also [[Generator of a category]].
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=Identity (disambiguation)=
 
=Identity (disambiguation)=
 
'''Identity''' may refer to
 
'''Identity''' may refer to
  
* An algebraic identity, an equation which is valid for all values of the variables involved, or some specified range of values, or [[Quasi-identity]]
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* An algebraic identity, an equality that holds true for all values of the variables involved within some domain of validity, or [[Quasi-identity]]
 
** [[Bianchi identity]]
 
** [[Bianchi identity]]
 
** [[Buchstab identity]]
 
** [[Buchstab identity]]
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** [[Capelli identity]]
 
** [[Capelli identity]]
 
** [[Polarisation identity]]
 
** [[Polarisation identity]]
* A mapping which sends an element to itself
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* A [[transformation]] which sends an element to itself
 
** [[Identity map]]
 
** [[Identity map]]
* An element of an algebraic structure which is neutral for an algebraic operation
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* An element of an algebraic structure which is a [[neutral element]] for an algebraic operation
 
** [[Identity element]]
 
** [[Identity element]]
 
*** [[Identity problem]]
 
*** [[Identity problem]]
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* An element of a [[trace monoid]]
 
* An element of a [[trace monoid]]
 
* [[Reduced trace]] on a central simple algebra
 
* [[Reduced trace]] on a central simple algebra
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* [[Dixmier trace]]
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** [[Wodzicki residue]] = Non-commutative residue

Latest revision as of 18:28, 28 February 2021

Generating set

Generating set may refer to

  • For an algebraic object $A$, a set $S$ such that the smallest subobject of $A$ containing $S$ is $A$ itself: a set $S$ such that $A$ consists of all elements resulting from applying the algebraic operations of $A$ to combinations of elements of $S$.
  • For the special cases of a free algebraic system on a given set of generators:

See also Generator of a category.

Identity (disambiguation)

Identity may refer to

Order (disambiguation)

The term "order" has far too many meanings for an article under that title to fix on a single one. There are at least three main groups of meanings:

Trace (disambiguation)

Trace may refer to

How to Cite This Entry:
Richard Pinch/sandbox-14. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Richard_Pinch/sandbox-14&oldid=51566