Fork me on GitHub
Math for the people, by the people.

User login

You are here

Home

Archimedean semigroup

Error message

  • User error: Socket error: Could not connect to "http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A15-01+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D" (proxy: 0): Connection refused in ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
  • User error: missing stream in "getFormat" via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
  • User error: missing stream in "readStream" http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A15-01+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).

Primary tabs

Archimedean semigroup

Let SSS be a commutative semigroup. We say an element xxx divides an element yyy, written x∣yfragmentsxnormal-∣yx\mid y, if there is an element zzz such that x⁢z=yxzyxz=y.

An Archimedean semigroup SSS is a commutative semigroup with the property that for all x,y∈SxySx,y\in S there is a natural number nnn such that x∣ynfragmentsxnormal-∣superscriptynx\mid y^{n}.

This is related to the Archimedean property of positive real numbers ℝ+superscriptℝ\mathbb{R}^{+}: if x,y>0xy0x,y>0 then there is a natural number nnn such that x<n⁢yxnyx<ny. Except that the notation is additive rather than multiplicative, this is the same as saying that (ℝ+)superscriptℝ(\mathbb{R}^{+},+) is an Archimedean semigroup.

Defines: 
divides, Archimedean
Related: 
ArchimedeanProperty
Type of Math Object: 
Definition
Major Section: 
Reference

Mathematics Subject Classification

20M14 no label found

Subscribe to Comments for "Archimedean semigroup"

Info

Owner: mclase
Added: 2002-11-05 - 23:38
Author(s): mclase

Versions

(v4) by mclase 2013-03-22
Powered By: = + + ♡