Ring of integers: Difference between revisions

Latest revision as of 16:24, 26 August 2024

This article is about a particular ring, i.e., a ring unique up to isomorphism. View a complete list of particular rings

The ring of integers, denoted $\mathbb {Z}$ , is the set of integers with addition and multiplication defined as for ordinary integers.

Property	Satisfied?	Explanation
integral domain	Yes
unique factorization domain	Yes	Fundamental Theorem of Arithmetic
principal ideal domain	Yes
Euclidean domain	Yes
field	No	No inverse of e.g. $2$

@@ Line 20: / Line 20: @@
 | [[satisfies property::Euclidean domain]] || Yes ||
 |-
-| [[satisfies property::field]] || No || No divisor of e.g. <math>2</math>
+| [[satisfies property::field]] || No || No inverse of e.g. <math>2</math>
 |}