/usr/share/axiom-20170501/src/algebra/ALGEBRA.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 21 22 | )abbrev category ALGEBRA Algebra
++ Description:
++ The category of associative algebras (modules which are themselves rings).
++
++ Axioms\br
++ \tab{5}\spad{(b+c)::% = (b::%) + (c::%)}\br
++ \tab{5}\spad{(b*c)::% = (b::%) * (c::%)}\br
++ \tab{5}\spad{(1::R)::% = 1::%}\br
++ \tab{5}\spad{b*x = (b::%)*x}\br
++ \tab{5}\spad{r*(a*b) = (r*a)*b = a*(r*b)}
Algebra(R) : Category == SIG where
R : CommutativeRing
SIG ==> Join(Ring, Module R) with
coerce : R -> %
++ coerce(r) maps the ring element r to a member of the algebra.
add
coerce(x:R):% == x * 1$%
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