Difference between revisions of "Regular module"
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| − | The '''regular left module''' of a [[ring]] <math>R</math> is | + | The '''regular left module''' of a [[ring]] <math>R</math> is the left <math>R</math>-[[module]] |
| − | whose underlying [[group]] is the additive group <math>R</math>, with multiplication | + | whose underlying [[group]] is the additive abelian group <math>R</math>, with multiplication |
given by left multiplication from <math>R</math>. The right regular module is defined | given by left multiplication from <math>R</math>. The right regular module is defined | ||
similarly. The left regular <math>R</math>-module is sometimes denoted | similarly. The left regular <math>R</math>-module is sometimes denoted | ||
Latest revision as of 10:53, 29 September 2012
The regular left module of a ring 
is the left -module
whose underlying group is the additive abelian group , with multiplication
given by left multiplication from . The right regular module is defined
similarly. The left regular -module is sometimes denoted
, and the right regular -module is sometimes denoted 
.
If is a commutative ring, then the two structures are the same
structure, called simply the regular -module.
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