/usr/share/axiom-20170501/src/algebra/LMODULE.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 20 | )abbrev category LMODULE LeftModule
++ Description:
++ The category of left modules over an rng
++ \spad{(ring not necessarily with unit)}.
++ This is an abelian group which supports left multiplication by elements of
++ the rng.
++
++ Axioms\br
++ \tab{5}\spad{(a*b)*x = a*(b*x)}\br
++ \tab{5}\spad{(a+b)*x = (a*x)+(b*x)}\br
++ \tab{5}\spad{a*(x+y) = (a*x)+(a*y)}
LeftModule(R) : Category == SIG where
R : Rng
SIG ==> AbelianGroup with
"*" : (R,%) -> %
++ r*x returns the left multiplication of the module element x
++ by the ring element r.
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