definition of greatest common divisors domain
Topics
About: ring
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
Starting Context
- The reader knows a definition of integral domain.
- The reader knows a definition of greatest common divisors of subset of commutative ring.
Target Context
- The reader will have a definition of greatest common divisors domain.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\(*R\): \(\in \{\text{ the integral domains }\}\)
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Conditions:
\(\forall \{p_1, p_2\} \subseteq R (gcd (\{p_1, p_2\}) \neq \emptyset)\)
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2: Natural Language Description
Any integral domain, \(R\), such that for each subset, \(\{p_1, p_2\} \subseteq R\), \(gcd (\{p_1, p_2\}) \neq \emptyset\)
