On Sun, 26 Feb 2006, Gabriel Dos Reis wrote:
In the impressive diagram titled "Basic Agebra Hierarchy" displayed
in the Axiom Book (I only have a copy of the edition copyrighted 1992,
NAG), AbelianSemiGroup is not "derived" from SemiGroup, and similarly
AbelianMonoid is not "derived" from Monoid. I find that curious as it
goes counter the mathematical fact that an AbelianMonoid *is* a
Monoid, with an additional algebraic law (commutation).
As far as I know, the reason is simple and purely notational. SemiGroup
has the binary operation *, and AbelianSemiGroup has +. Therefore, it
cannot be derived from SemiGroup. But some other categories can be derived
from both of them, inheriting * (maybe non-commutative) from SemiGroup and
+ (always commutative) from AbelianSemiGroup.
My copy of the Axiom book is in my office, and I am writing from home, so,
details may be wrong.
Andrey
_______________________________________________
Axiom-developer mailing list
[email protected]
http://lists.nongnu.org/mailman/listinfo/axiom-developer
