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5
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Why $r \notin R^*$ if it is a prime? [duplicate]
My professor gave us the following definition:
Let $R$ be a commutative ring. $r \in R$ is prime if $r.R$ is a prime ideal. Then he concluded that this definition tells us $r \notin R^*$ but I do not ...
user778657
3
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Does every commutative ring with $1 \neq 0$ and a non-zero, non-unit element contain a prime element?
As above, I am trying to answer the following question:
"Does every commutative ring with $1 \neq 0$ and a non-zero, non-unit element contain a prime element?"
Since in some books prime elements are ...
- 4,899
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minimality of ideals generated by primes among the prime ideals
I have following task:
Given a factorial ring $R$ (i.e. with unique prime decomposition) and a prime element $a \in R$ prove that if $I \subseteq R$ is a prime ideal with $(0) \subseteq I \subseteq ...
- 16.7k
5
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3
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183
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Sanity check on factorization of $\langle 5 \rangle$ in $\mathbb{Z}_{10}$
Looking at $\mathbb{Z}_{10}$, consisting of $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ with addition and multiplication adjusted so the ring is closed under both operations.
Clearly $5 = 3 \times 5 = 5 \times 5 =...
- 1,108
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Is every polynomial with integer coefficients prime in $\mathbb{Z}[x]$ also prime in $\mathbb{Q}[x]$? [closed]
The question is as in the title:
Is every polynomial with integer coefficients prime in $\mathbb{Z}[x]$ also prime in $\mathbb{Q}[x]$?
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