| http://dbpedia.org/ontology/abstract
|
In mathematics, Brandt semigroups are comp … In mathematics, Brandt semigroups are completely 0-simple inverse semigroups. In other words, they are semigroups without proper ideals and which are also inverse semigroups. They are built in the same way as completely 0-simple semigroups: Let G be a group and be non-empty sets. Define a matrix of dimension with entries in Then, it can be shown that every 0-simple semigroup is of the form with the operation . As Brandt semigroups are also inverse semigroups, the construction is more specialized and in fact, I = J (Howie 1995). Thus, a Brandt semigroup has the form with the operation . Moreover, the matrix is diagonal with only the identity element e of the group G in its diagonal. element e of the group G in its diagonal.
|
| http://dbpedia.org/ontology/wikiPageID
|
32042560
|
| http://dbpedia.org/ontology/wikiPageLength
|
1831
|
| http://dbpedia.org/ontology/wikiPageRevisionID
|
1104743395
|
| http://dbpedia.org/ontology/wikiPageWikiLink
|
http://dbpedia.org/resource/Heinrich_Brandt +
, http://dbpedia.org/resource/Category:Semigroup_theory +
, http://dbpedia.org/resource/Semigroup +
, http://dbpedia.org/resource/Special_classes_of_semigroups +
, http://dbpedia.org/resource/Inverse_semigroup +
, http://dbpedia.org/resource/Group_%28mathematics%29 +
|
| http://dbpedia.org/property/wikiPageUsesTemplate
|
http://dbpedia.org/resource/Template:Citation +
, http://dbpedia.org/resource/Template:Abstract-algebra-stub +
|
| http://purl.org/dc/terms/subject
|
http://dbpedia.org/resource/Category:Semigroup_theory +
|
| http://www.w3.org/ns/prov#wasDerivedFrom
|
http://en.wikipedia.org/wiki/Brandt_semigroup?oldid=1104743395&ns=0 +
|
| http://xmlns.com/foaf/0.1/isPrimaryTopicOf
|
http://en.wikipedia.org/wiki/Brandt_semigroup +
|
| owl:sameAs |
https://global.dbpedia.org/id/4bh7M +
, http://dbpedia.org/resource/Brandt_semigroup +
, http://www.wikidata.org/entity/Q4957188 +
, http://rdf.freebase.com/ns/m.0gwz864 +
|
| rdfs:comment |
In mathematics, Brandt semigroups are comp … In mathematics, Brandt semigroups are completely 0-simple inverse semigroups. In other words, they are semigroups without proper ideals and which are also inverse semigroups. They are built in the same way as completely 0-simple semigroups: Let G be a group and be non-empty sets. Define a matrix of dimension with entries in Then, it can be shown that every 0-simple semigroup is of the form with the operation . As Brandt semigroups are also inverse semigroups, the construction is more specialized and in fact, I = J (Howie 1995). Thus, a Brandt semigroup has the form with the operation .emigroup has the form with the operation .
|
| rdfs:label |
Brandt semigroup
|
