Modules As External Rings
Much of the machinery of modules and vector spaces are fairly straightforward, or discussed above. The only thing not covered yet is their distribution axioms. The external ring multiplication is externally distributive in over the ring iff:
- for all and:
- for all
Using these terminology we can make the following local generalizations:
- An external semiring over the semiring is a commutative monoid and an external monoid where is externally distributive in over the semiring .
- An external ring over the ring is an Abelian group and an external monoid where is externally distributive in over the ring .
Read more about this topic: External (mathematics)
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