Toscead betweox fadungum "Rīmagiefung"

 

Þæt dǣl stæfrīmtācninge gehāten [[grundstaðoliende stæfrīmtācning]] is oft dǣl þǣre lāre in [[ōðerlic lǣrung|ōðerlicre lǣrunge]] and inlǣdeþ þā oncnāwnesse [[missenrīm (on rīmcræfte)|missenrīma]] þe tācniaþ [[rīm]]. Cwidas gestaðolode on þissum missenrīmum sind gestēorede notiende þā laga weorcinga þā mann mæg wyrcan mid rīmum, swelce [[ēacnung (on rīmcræfte)]]. Þis mæg wesan gedōn for missenlicum intingum, befōnde [[efenweorþfindung]]. Stæfrīmtācning is swīðe brādre þonne grundstaðoliende stæfrīmtācning; hēo is sēo cnēorlǣcing þæs gelimpeþ þǣr missenlica laga weorcinge sind gebrocen and þǣr weorcinga sind worht tō ōðrum þingum ōðer rīm. <!--Ēacnung and [[manigfealding]] cunnon wesan brǣded and heora forrihtan tōmearcunga inlǣdaþ [[stæfrīmtācningisc timber|stæfrīmtācningisce timbras]] swelce [[þrēat (on rīmlāre)|þrēatas]], [[hring (on rīmlāre)|hringas]] and [[feld (on rīmlāre)|felda]], þe sind cnēorlǣht on þǣm dǣle rīmlāre þe hāteþ [[brād stæfrīmtācing]].

'''[[Commutative operation|Commutativity]]''': Addition of integers also has a property called commutativity. That is, the order of the numbers to be added does not affect the sum. For example: 2+3=3+2. In general, this becomes ''a'' ∗ ''b'' = ''b'' ∗ ''a''. Only some binary operations have this property. It holds for the integers with addition and multiplication, but it does not hold for [[matrix multiplication]] or [[Quaternion|quaternion multiplication]] .

 

{{main|Group (mathematics)}} {{see also|Group theory|Examples of groups}}

 

All groups are monoids, and all monoids are semigroups.

 

{{main|ring (mathematics)|field (mathematics)}} {{see also|Ring theory|Glossary of ring theory|Field theory (mathematics)|glossary of field theory}}

 

* I.N. Herstein: ''Topics in Algebra''. ISBN 0-471-02371-X

* R.B.J.T. Allenby: ''Rings, Fields and Groups''. ISBN 0-340-54440-6

* Isaac Asimov ''Realm of Algebra'' (Houghton Mifflin), 1961-->

 

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