# Category:Principal Ideal Domains

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This category contains results about Principal Ideal Domains.

A **principal ideal domain** is an integral domain in which every ideal is a principal ideal.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Principal Ideal Domains"

The following 23 pages are in this category, out of 23 total.

### E

### G

### P

- Polynomial Forms is PID Implies Coefficient Ring is Field
- Polynomial Forms over Field form Principal Ideal Domain
- Polynomials in Integers is not Principal Ideal Domain
- Prime Ideal of Principal Ideal Domain is Maximal
- Principal Ideal Domain cannot have Infinite Strictly Increasing Sequence of Ideals
- Principal Ideal Domain fulfills Ascending Chain Condition
- Principal Ideal Domain is Bézout Domain
- Principal Ideal Domain is Dedekind Domain
- Principal Ideal Domain is Integrally Closed
- Principal Ideal Domain is Unique Factorization Domain
- Principal Ideal of Principal Ideal Domain is of Irreducible Element iff Maximal