carten.spad line 1 [edit on github]
GradedModule(R
, E
) denotes ``E-graded R
-module''
, i.e. collection of R
-modules indexed by an abelian monoid E
. An element g
of G[s]
for some specific s
in E
is said to be an element of G
with degree s
. Sums are defined in each module G[s]
so two elements of G
have a sum if they have the same degree. Morphisms can be defined and composed by degree to give the mathematical category of graded modules.
g*r
is right module multiplication.
r*g
is left module multiplication.
g+h
is the sum of g
and h
in the module of elements of the same degree as g
and h
. Error: if g
and h
have different degrees.
-g
is the additive inverse of g
in the module of elements of the same grade as g
.
g-h
is the difference of g
and h
in the module of elements of the same degree as g
and h
. Error: if g
and h
have different degrees.
0 denotes the zero of degree 0.
degree(g)
names the degree of g
. The set of all elements of a given degree form an R
-module.