The subring generated by is formed by finite sums of monomials of the form :
Of particular interest is the subring generated by a family of subrings . It is the ring formed by finite sums of monomials of the form:
If are rings, the subring generated by is also denoted by .
In the case when are fields included in a larger field then the set of all quotients of elements of ( the quotient field of ) is the composite field of the family . In other words, it is the subfield generated by . The notation comes from the fact that the family of all subfields of a field forms a complete lattice.
The of fields is defined only when the respective fields are all included in a larger field.
|Date of creation||2013-03-22 16:57:27|
|Last modified on||2013-03-22 16:57:27|
|Last modified by||polarbear (3475)|
|Defines||subring generated by|
|Defines||monomials in rings|