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Mare
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Question 1: Is there a classification of (noetherian if needed) integral domains with finitely many units ? (of course we can exclude fields as trivial examples)

Probably there are many such domains that I can not think of but maybe there is an overview article of what is known.

Question 2: Is there a classification of principal ideal domains with finitelym any units?

This seems to be much more restrictive. Examples include the (finitely many) imaginary quadratic fields with class number one and $F_q[x]$ for finite fields $F_q$.

If it helps one can also assume some additional things like characteristic 0.

Question 1: Is there a classification of (noetherian if needed) integral domains with finitely many units ? (of course we can exclude fields as trivial examples)

Probably there are many such domains that I can not think of but maybe there is an overview article of what is known.

Question 2: Is there a classification of principal ideal domains with finitelym any units?

This seems to be much more restrictive. Examples include the (finitely many) imaginary quadratic fields with class number one and $F_q[x]$ for finite fields $F_q$.

If it helps one can also assume some additional things like characteristic 0.

Question: Is there a classification of (noetherian if needed) integral domains with finitely many units ? (of course we can exclude fields as trivial examples)

Probably there are many such domains that I can not think of but maybe there is an overview article of what is known.

If it helps one can also assume some additional things like characteristic 0.

Source Link
Mare
Mare
  • 26.5k
  • 6
  • 25
  • 104

Integral domains with finitely many units

Question 1: Is there a classification of (noetherian if needed) integral domains with finitely many units ? (of course we can exclude fields as trivial examples)

Probably there are many such domains that I can not think of but maybe there is an overview article of what is known.

Question 2: Is there a classification of principal ideal domains with finitelym any units?

This seems to be much more restrictive. Examples include the (finitely many) imaginary quadratic fields with class number one and $F_q[x]$ for finite fields $F_q$.

If it helps one can also assume some additional things like characteristic 0.