Commutative algebra Domains and factorization Concept
Principal ideal domain
Summary
A principal ideal domain is an integral domain in which every ideal is generated by one element. The integers and the polynomials over a field are examples. The definition of a principal ideal domain gives the conditions.
Where this leads
10 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/Principal_ideal_domain, lead section
About this page
| Tag | 0CMD0BCH8T |
|---|---|
| URI | m2://0CMD0BCH8T |
| Aliases | pid |
| Kind | concept |
| Writing | W1 stated |
| MSC | 13F10 |
| Specializes | Unique factorisation domain |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Special cases
Definitions
Used by
- Discrete valuation ring
- Künneth theorem
- Quillen–Suslin theorem
- Flat module
- Universal coefficient theorem
- Smith normal form
- Injective module
- Structure theorem for finitely generated modules over a principal ideal domain
- A Dedekind UFD is a PID