PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: Medium Entry average rating: No information on entry rating
rig (Definition)

A rig $ (R, +, \cdot)$ is a set $ R$ together with two binary operations $ +:R^2 \to R:(a, b) \mapsto a + b$ and $ \cdot:R^2 \to R:(a, b) \mapsto ab$, such that both $ (R, +)$ and $ (R, \cdot)$ are monoids, where $ \cdot$ distributes over $ +$. That is if $ \{a, b, c, d\} \subset R$ then $ (a+b)(c+d) = ac + ad + bc +bd$. The natural numbers with ordinary addition and multiplication $ (\mathbf{N}, +, \cdot)$ is a rig.

A rig $ (R, +, \cdot)$ is a ring if $ (R, +)$ is a group. The integers with ordinary addition and multiplication $ (\mathbf{Z}, +, \cdot)$ is a ring.



Anyone with an account can edit this entry. Please help improve it!

"rig" is owned by HkBst.
(view preamble)

View style:

See Also: semigroup, ring

Log in to rate this entry.
(view current ratings)

Cross-references: integers, group, ring, multiplication, addition, natural numbers, distributes over, monoids, binary operations
There are 3 references to this entry.

This is version 5 of rig, born on 2004-10-16, modified 2006-09-15.
Object id is 6378, canonical name is Rig.
Accessed 2099 times total.

Classification:
AMS MSC20M99 (Group theory and generalizations :: Semigroups :: Miscellaneous)

Pending Errata and Addenda
None.
[ View all 5 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)