About: Cancellative semigroup

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

About: Cancellative semigroup Goto Sponge NotDistinct Permalink

An Entity of Type : yago:WikicatAlgebraicStructures, within Data Space : dbpedia.org associated with source document(s)
QRcode icon

http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FCancellative_semigroup

In mathematics, a cancellative semigroup (also called a cancellation semigroup) is a semigroup having the cancellation property. In intuitive terms, the cancellation property asserts that from an equality of the form a·b = a·c, where · is a binary operation, one can cancel the element a and deduce the equality b = c. In this case the element being cancelled out is appearing as the left factors of a·b and a·c and hence it is a case of the left cancellation property. The right cancellation property can be defined analogously. Prototypical examples of cancellative semigroups are the positive integers under addition or multiplication. Cancellative semigroups are considered to be very close to being groups because cancellability is one of the necessary conditions for a semigroup to be embeddabl

Attributes	Values
rdf:type	yago:Artifact100021939 yago:Object100002684 yago:PhysicalEntity100001930 yago:YagoGeoEntity yago:YagoPermanentlyLocatedEntity yago:Structure104341686 yago:Whole100003553 yago:WikicatAlgebraicStructures
rdfs:label	Cancellative semigroup (en)
rdfs:comment	In mathematics, a cancellative semigroup (also called a cancellation semigroup) is a semigroup having the cancellation property. In intuitive terms, the cancellation property asserts that from an equality of the form a·b = a·c, where · is a binary operation, one can cancel the element a and deduce the equality b = c. In this case the element being cancelled out is appearing as the left factors of a·b and a·c and hence it is a case of the left cancellation property. The right cancellation property can be defined analogously. Prototypical examples of cancellative semigroups are the positive integers under addition or multiplication. Cancellative semigroups are considered to be very close to being groups because cancellability is one of the necessary conditions for a semigroup to be embeddabl (en)
dcterms:subject	Semigroup theory Algebraic structures
Wikipage page ID	22772051 (xsd:integer)
Wikipage revision ID	1124117022 (xsd:integer)
Link from a Wikipage to another Wikipage	Epigroup Nonsingular Null semigroup Semigroup theory Commutative Mathematics Matrix (mathematics) Matrix multiplication Equality (mathematics) Monoid Multiplication Ore condition Subsemigroup Embedding Mathematische Annalen Algebraic structures Semigroup Square matrix Addition American Mathematical Society Group (mathematics) Special classes of semigroups Abelian group Binary operation Positive integer Field of fractions Grothendieck group Group theory If and only if Natural number Cancellation property Real number Injective Right zero semigroup Semigroup homomorphism Left zero semigroup
Link from a Wikipage to an external page	http://www.gap-system.org/~history/Extras/Preston_semigroups.html https://web.archive.org/web/20090109045100/http:/www.gap-system.org/~history/Extras/Preston_semigroups.html%23
sameAs	Cancellative semigroup Cancellative semigroup Cancellative semigroup Cancellative semigroup Cancellative semigroup
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harv dbt:Reflist
has abstract	In mathematics, a cancellative semigroup (also called a cancellation semigroup) is a semigroup having the cancellation property. In intuitive terms, the cancellation property asserts that from an equality of the form a·b = a·c, where · is a binary operation, one can cancel the element a and deduce the equality b = c. In this case the element being cancelled out is appearing as the left factors of a·b and a·c and hence it is a case of the left cancellation property. The right cancellation property can be defined analogously. Prototypical examples of cancellative semigroups are the positive integers under addition or multiplication. Cancellative semigroups are considered to be very close to being groups because cancellability is one of the necessary conditions for a semigroup to be embeddable in a group. Moreover, every finite cancellative semigroup is a group. One of the main problems associated with the study of cancellative semigroups is to determine the necessary and sufficient conditions for embedding a cancellative semigroup in a group. The origins of the study of cancellative semigroups can be traced to the first substantial paper on semigroups,. (en)
gold:hypernym	Semigroup
prov:wasDerivedFrom	wikipedia-en:Cancellative_semigroup?oldid=1124117022&ns=0
page length (characters) of wiki page	11971 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Cancellative_semigroup
is Link from a Wikipage to another Wikipage of	Epigroup GCD domain Semigroup Special classes of semigroups Division by zero Cancellation property Variety (universal algebra) Stable theory Quasivariety Cancellation semigroup
is Wikipage redirect of	Cancellation semigroup
is foaf:primaryTopic of	wikipedia-en:Cancellative_semigroup

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (62 GB total memory, 54 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software