Difference between revisions of "Template:Abstract algebra navbox"
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(Created page with "{{Navbox |name=Abstract algebra navbox |style= border: 1px solid #aaa;width: 100%;margin: auto;clear: both;font-size: 88%;text-align: center;padding: 1px; background: #fdfdfd...") |
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{{Navbox | {{Navbox | ||
|name=Abstract algebra navbox | |name=Abstract algebra navbox | ||
| + | |state={{#if:{{{1|}}}|{{{1|}}}|<noinclude>plain</noinclude>}} | ||
|style= border: 1px solid #aaa;width: 100%;margin: auto;clear: both;font-size: 88%;text-align: center;padding: 1px; background: #fdfdfd; | |style= border: 1px solid #aaa;width: 100%;margin: auto;clear: both;font-size: 88%;text-align: center;padding: 1px; background: #fdfdfd; | ||
|groupstyle= white-space: nowrap; text-align: right; font-weight: bold; padding-left: 1em; padding-right: 1em;background: #ddddff; | |groupstyle= white-space: nowrap; text-align: right; font-weight: bold; padding-left: 1em; padding-right: 1em;background: #ddddff; | ||
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|abovestyle=background: #ddddff; | |abovestyle=background: #ddddff; | ||
|title=Abstract algebra | |title=Abstract algebra | ||
| − | |above=Overview of the basic and important objects of [[Abstract | + | |above=Overview of the basic and important objects of [[Abstract Algebra (subject)|abstract algebra]] |
|group1=Single [[Binary operation|operation]] objects | |group1=Single [[Binary operation|operation]] objects | ||
|list1=[[semigroup]] {{M|\supset}} [[monoid]] {{M|\supset}} [[group]] | |list1=[[semigroup]] {{M|\supset}} [[monoid]] {{M|\supset}} [[group]] | ||
|group2=[[Commutative]] single operation objects | |group2=[[Commutative]] single operation objects | ||
| − | |list2=[[Abelian monoid]] {{M|\supset}} [[Abelian group]] | + | |list2=[[Abelian semigroup]] [[Abelian monoid]] {{M|\supset}} [[Abelian group]] |
| + | |group3=Related objects of semigroups<br/><span style="font-weight:normal">(thus all monoids and groups too)</span> | ||
| + | |list3='''Entire semigroup: ''' [[Centre]], [[Subsemigroup]], [[Order (semigroup)|Order]]<br/>'''Of subset: ''' [[Centraliser]], [[Stable|stability]], [[Generator (semigroup, subset)|Generator]] <br/>'''Of element: '''[[Orbit]], [[Generator (semigroup, element)|Generator]], [[Order (semigroup, element)|Order]] | ||
| + | |group4=Related objects of monoids<br/><span style="font-weight:normal">(thus all groups too)</span> | ||
| + | |list4=[[Submonoid]] | ||
| + | |group5=Related objects of groups | ||
| + | |list5=[[Subgroup]], [[Normal subgroup]], [[Index (group)|Index]] | ||
| + | |group6=Important semigroup theorems | ||
| + | |list6= | ||
| + | |group7=Important monoid theorems | ||
| + | |list7= | ||
| + | |group8=Important group theorems | ||
| + | |list8=[[Group isomorphism theorems|3 isomorphism theorems]], [[Butterfly lemma]] | ||
| + | |group9=Mappings between semigroups<br/><span style="font-weight:normal">(thus between monoids and groups too)</span> | ||
| + | |list9=[[Semigroup homomorphism|Homomorphism]], [[Set of homomorphisms (semigroup)|The set {{M|\text{Hom}(X,Y)}} of homomorphisms between {{M|X}} and {{M|Y}}]], [[Semigroup morphisms|Other morphisms]] | ||
| + | |group10=Constructing new semigroups from old | ||
| + | |list10=[[Direct product (semigroups)|Direct product]], [[Direct sum (semigroups)|Direct sum]] | ||
| + | |group11=Group constructions | ||
| + | |list11=[[Quotient (group)|Quotient group]] | ||
| + | |group12=Objects related to mappings between groups | ||
| + | |list12=[[Image (group homomorphism)|Image]], [[Kernel (group homomorphism)|Kernel]] | ||
}}<noinclude> | }}<noinclude> | ||
[[Category:Navboxes]] | [[Category:Navboxes]] | ||
[[Category:Abstract Algebra]] | [[Category:Abstract Algebra]] | ||
{{Todo|fill this out}} | {{Todo|fill this out}} | ||
| + | {{Todo|This is very "group-like" at the moment (1/2/2015 @ 1730), perhaps splitting it into other navboxes would be good}} | ||
| + | {{Todo|Decide on a term for things like "homomorphism" of these group like structures, semigroup seems to be the "highest parent type" thus "homomorphism (semigroup)" is a good candidate, however "homomorphism (group-like structure)" is perhaps better}} | ||
| + | {{ProjectTodo|Navbox project|Get this fixed}} | ||
</noinclude> | </noinclude> | ||
Latest revision as of 11:26, 20 February 2016
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TODO: fill this out
TODO: This is very "group-like" at the moment (1/2/2015 @ 1730), perhaps splitting it into other navboxes would be good
TODO: Decide on a term for things like "homomorphism" of these group like structures, semigroup seems to be the "highest parent type" thus "homomorphism (semigroup)" is a good candidate, however "homomorphism (group-like structure)" is perhaps better
Todo (Navbox project): Get this fixed
