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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJul 18th 2014

needed to point to ring of integers of a number field. The term used to redirect just to integers. I have split it off now with a minimum of content. Have to rush off now.

• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeJul 18th 2014

Fixed a mathematical typo and added a little more to the Idea section.

• CommentRowNumber3.
• CommentAuthorTobyBartels
• CommentTimeJul 18th 2014
• (edited Jul 18th 2014)

I made integer link to ring of integers in the Terminology section.

But we also have algebraic integer (written primarily by Todd) ,which seems to cover much the same ground. (It even has the boldface term ‘ring of integers’ in it, so the redirect probably should have been there all along.)

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJul 19th 2014

Oh, I didn’t see this, sorry. Should be merged.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeJul 19th 2014

Btw, thanks for fixing my text. I suppose I left out the condition that the coefficients are integra.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJul 19th 2014

I gave both algebraic integer and ring of integers a brief Idea-section to help the reader with getting an idea of what’s going on before diving into the technical details. Please check if you agree and feel invited to edit as need be.

• CommentRowNumber7.
• CommentAuthorTobyBartels
• CommentTimeJul 19th 2014

Do you still want to merge them?

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeJul 19th 2014

I wouldn’t mind, but I don’t feel like doing it myself. If you want to, please do!

• CommentRowNumber9.
• CommentAuthorTobyBartels
• CommentTimeJul 20th 2014

I probably will then, but not on this lousy phone!

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeJul 21st 2014
• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeJul 21st 2014

And I have expanded the Idea-sentence just a little and added two more simple examples in the Example-section.

• CommentRowNumber12.
• CommentAuthorzskoda
• CommentTimeNov 10th 2016
• (edited Nov 10th 2016)

I made a number of changes in ring of integers. Namely the entry had the format which sugested that the definitions in a number field and in a local nonarchimedean field are different and did not include other cases. I made it the standard way with easy general definition in an arbitrary commutative unital ring. The special cases are now under notation and properties as it should be.

• CommentRowNumber13.
• CommentAuthorDavidRoberts
• CommentTimeNov 10th 2016

I added a reference at ring of integers to the recently published paper Defining $\mathbb{Z}$ in $\mathbb{Q}$.

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeOct 7th 2018

added to the list of examples:

The ring of intergers of a cyclotomic field $\mathbb{Q}(\zeta_n)$ is $\mathbb{Z}[\zeta_n]$, called the ring of cyclotomic integers.