Notation regarding polynomial ideals

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Suppose $F[x]$ is a field, and $p(x) in F[x]$ be a polynomial. We want to quotient $F[x]$ with the ideal generated by $p(x)$.



While the commonly used notation to denote that $F[x]/p(x)$, isn't the notation kinda misleading because $p(x)$ is not an ideal ?



I think $F[x]/p(x)F[x]$ should be the correct notation since $p(x)F[x]$ is an ideal.




abstract-algebra notation




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  • 5




    You also can use $F[x]/bigl(p(x)bigr)$.
    – Bernard
    Jul 25 at 16:29










  • The same problem ("kinda misleading"?) is with $BbbZ/n$ or $BbbZ/(n)$ or $BbbZ/nBbbZ$. Even worse, $BbbZ_p$, which are also $p$-adic integers.
    – Dietrich Burde
    Jul 25 at 19:38















up vote
0
down vote

favorite












Suppose $F[x]$ is a field, and $p(x) in F[x]$ be a polynomial. We want to quotient $F[x]$ with the ideal generated by $p(x)$.



While the commonly used notation to denote that $F[x]/p(x)$, isn't the notation kinda misleading because $p(x)$ is not an ideal ?



I think $F[x]/p(x)F[x]$ should be the correct notation since $p(x)F[x]$ is an ideal.




abstract-algebra notation




share|cite|improve this question















  • 5




    You also can use $F[x]/bigl(p(x)bigr)$.
    – Bernard
    Jul 25 at 16:29










  • The same problem ("kinda misleading"?) is with $BbbZ/n$ or $BbbZ/(n)$ or $BbbZ/nBbbZ$. Even worse, $BbbZ_p$, which are also $p$-adic integers.
    – Dietrich Burde
    Jul 25 at 19:38













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Suppose $F[x]$ is a field, and $p(x) in F[x]$ be a polynomial. We want to quotient $F[x]$ with the ideal generated by $p(x)$.



While the commonly used notation to denote that $F[x]/p(x)$, isn't the notation kinda misleading because $p(x)$ is not an ideal ?



I think $F[x]/p(x)F[x]$ should be the correct notation since $p(x)F[x]$ is an ideal.




abstract-algebra notation




share|cite|improve this question











Suppose $F[x]$ is a field, and $p(x) in F[x]$ be a polynomial. We want to quotient $F[x]$ with the ideal generated by $p(x)$.



While the commonly used notation to denote that $F[x]/p(x)$, isn't the notation kinda misleading because $p(x)$ is not an ideal ?



I think $F[x]/p(x)F[x]$ should be the correct notation since $p(x)F[x]$ is an ideal.





abstract-algebra notation





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 25 at 16:26









alxchen

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  • 5




    You also can use $F[x]/bigl(p(x)bigr)$.
    – Bernard
    Jul 25 at 16:29










  • The same problem ("kinda misleading"?) is with $BbbZ/n$ or $BbbZ/(n)$ or $BbbZ/nBbbZ$. Even worse, $BbbZ_p$, which are also $p$-adic integers.
    – Dietrich Burde
    Jul 25 at 19:38













  • 5




    You also can use $F[x]/bigl(p(x)bigr)$.
    – Bernard
    Jul 25 at 16:29










  • The same problem ("kinda misleading"?) is with $BbbZ/n$ or $BbbZ/(n)$ or $BbbZ/nBbbZ$. Even worse, $BbbZ_p$, which are also $p$-adic integers.
    – Dietrich Burde
    Jul 25 at 19:38








5




5




You also can use $F[x]/bigl(p(x)bigr)$.
– Bernard
Jul 25 at 16:29




You also can use $F[x]/bigl(p(x)bigr)$.
– Bernard
Jul 25 at 16:29












The same problem ("kinda misleading"?) is with $BbbZ/n$ or $BbbZ/(n)$ or $BbbZ/nBbbZ$. Even worse, $BbbZ_p$, which are also $p$-adic integers.
– Dietrich Burde
Jul 25 at 19:38





The same problem ("kinda misleading"?) is with $BbbZ/n$ or $BbbZ/(n)$ or $BbbZ/nBbbZ$. Even worse, $BbbZ_p$, which are also $p$-adic integers.
– Dietrich Burde
Jul 25 at 19:38
















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