/usr/share/axiom-20170501/src/algebra/RMODULE.spad is in axiom-source 20170501-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | )abbrev category RMODULE RightModule
++ Description:
++ The category of right modules over an rng (ring not necessarily
++ with unit). This is an abelian group which supports right
++ multiplication by elements of the rng.
++
++ Axioms\br
++ \tab{5}\spad{x*(a*b) = (x*a)*b}\br
++ \tab{5}\spad{x*(a+b) = (x*a)+(x*b)}\br
++ \tab{5}\spad{(x+y)*x = (x*a)+(y*a)}
RightModule(R) : Category == SIG where
R : Rng
SIG ==> AbelianGroup with
"*" : (%,R) -> %
++ x*r returns the right multiplication of the module element x
++ by the ring element r.
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