distributivity (original) (raw)
Given a set (http://planetmath.org/Set) S with two binary operations
+:S×S→S and ⋅:S×S→S, we say that ⋅ is right distributive over + if
| (a+b)⋅c=(a⋅c)+(b⋅c)foralla,b,c∈S |
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and left distributive over + if
| a⋅(b+c)=(a⋅b)+(a⋅c)foralla,b,c∈S. |
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If ⋅ is both left and right distributive over +, then it is said to be distributive over + (or, alternatively, we may say that ⋅ distributes over +).
| Title | distributivity |
|---|---|
| Canonical name | Distributivity |
| Date of creation | 2013-03-22 13:47:00 |
| Last modified on | 2013-03-22 13:47:00 |
| Owner | yark (2760) |
| Last modified by | yark (2760) |
| Numerical id | 15 |
| Author | yark (2760) |
| Entry type | Definition |
| Classification | msc 06D99 |
| Classification | msc 16-00 |
| Classification | msc 13-00 |
| Classification | msc 17-00 |
| Synonym | distributive law |
| Synonym | distributive property |
| Related topic | Ring |
| Related topic | DistributiveLattice |
| Related topic | NearRing |
| Defines | distributive |
| Defines | left distributive |
| Defines | right distributive |
| Defines | left-distributive |
| Defines | right-distributive |
| Defines | distributes over |
| Defines | left distributivity |
| Defines | right distributivity |
| Defines | left distributes over |
| Defines | left distributive law |
| Defines | right distributive law |