Difference between revisions of "Regular module"
(Created page with 'The '''regular left module''' of a ring <math>R</math> is the the left <math>R</math>-module whose underlying group is the additive group <math>R</math>, with multipl…') |
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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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