41.18 Row Module Records

Module records contain at least the components

isDomain :

always true,

isModule :

always true,

isVectorSpace :

always true, since modules are vector spaces,

ring :

the ring acting on the module,

field :

the coefficients field, is the same as R.field where R is the ring component of the module,

operations :

the operations record of the module.

The following components are optional, but if they are not present then the corresponding function in the operations record must know how to compute them.

generators :

a list of module generators (not necessarily of vector space generators),

zero :

the zero element of the module.

basis :

a vector space basis of the module (see also Row Space Bases),

Factors of row modules have the same components as quotients of row spaces (see Quotient Space Records), except that of course they have an appropriate operations record.

Additionally factors of row modules have the components isModule, isFactorModule (both always true). Parent modules also have the ring component, which is the same ring as the ring component of numerator and denominator.

Previous Up Top Next
Index