finitely generated module
A module over a ring is said to be finitely generated if there is a finite subset of such that spans . Let us recall that the span of a (not necessarily finite) set of vectors is the class of all (finite) linear combinations of elements of ; moreover, let us recall that the span of the empty set is defined to be the singleton consisting of only one vector, the zero vector . A module is then called cyclic if it can be a singleton.
Examples. Let be a commutative ring with 1 and be an indeterminate.
is a cyclic -module generated by .
is a finitely-generated -module generated by . Any element in can be expressed uniquely as .
|Title||finitely generated module|
|Date of creation||2013-03-22 14:01:08|
|Last modified on||2013-03-22 14:01:08|
|Owner||Thomas Heye (1234)|
|Last modified by||Thomas Heye (1234)|
|Author||Thomas Heye (1234)|