RightModule(R)

catdef.spad line 1329 [edit on github]

• R : SemiRng

The category of right modules over an rng (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the rng.

* : (%, R) -> %

x*r returns the right multiplication of the module element x by the ring element r.

* : (Integer, %) -> % if R has AbelianGroup

from AbelianGroup

* : (NonNegativeInteger, %) -> % if R has AbelianMonoid

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> % if R has AbelianGroup

from AbelianGroup

- : (%, %) -> % if R has AbelianGroup

from AbelianGroup

0 : () -> % if R has AbelianMonoid

from AbelianMonoid

= : (%, %) -> Boolean

from BasicType

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

latex : % -> String

from SetCategory

opposite? : (%, %) -> Boolean if R has AbelianMonoid

from AbelianMonoid

sample : () -> % if R has AbelianMonoid

from AbelianMonoid

subtractIfCan : (%, %) -> Union(%, "failed") if R has AbelianGroup

from CancellationAbelianMonoid

zero? : % -> Boolean if R has AbelianMonoid

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

CancellationAbelianMonoid

CoercibleTo(OutputForm)

AbelianMonoid

AbelianSemiGroup

SetCategory

BasicType

AbelianGroup