Is $S$ is subring of $T$?











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consider $S = C[x^5]$,complex polynomials is $x^5$ , as a subset of $T =C[x]$ the ring of all complex polynomials.
Now My question is that



Is $S$ is subring of $T$ ?



My attempts : i Thinks Yes because $S$ is a subset of $T$



Any hints/solution will be apprecaited



thanks u






abstract-algebra







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  • 4




    Check also $S$ is closed under subtraction, closed under multiplication, and it contains the multiplicative identity $1$.
    – i707107
    Nov 19 at 22:27






  • 1




    Its a subset but as said, you need to check that it is closed under addition, contains the additive inverse of each element, it is closed under multiplication and contains the unit element 1.
    – Wuestenfux
    Nov 20 at 12:09















up vote
0
down vote

favorite












consider $S = C[x^5]$,complex polynomials is $x^5$ , as a subset of $T =C[x]$ the ring of all complex polynomials.
Now My question is that



Is $S$ is subring of $T$ ?



My attempts : i Thinks Yes because $S$ is a subset of $T$



Any hints/solution will be apprecaited



thanks u






abstract-algebra







share|cite|improve this question


















  • 4




    Check also $S$ is closed under subtraction, closed under multiplication, and it contains the multiplicative identity $1$.
    – i707107
    Nov 19 at 22:27






  • 1




    Its a subset but as said, you need to check that it is closed under addition, contains the additive inverse of each element, it is closed under multiplication and contains the unit element 1.
    – Wuestenfux
    Nov 20 at 12:09













up vote
0
down vote

favorite









up vote
0
down vote

favorite











consider $S = C[x^5]$,complex polynomials is $x^5$ , as a subset of $T =C[x]$ the ring of all complex polynomials.
Now My question is that



Is $S$ is subring of $T$ ?



My attempts : i Thinks Yes because $S$ is a subset of $T$



Any hints/solution will be apprecaited



thanks u






abstract-algebra







share|cite|improve this question













consider $S = C[x^5]$,complex polynomials is $x^5$ , as a subset of $T =C[x]$ the ring of all complex polynomials.
Now My question is that



Is $S$ is subring of $T$ ?



My attempts : i Thinks Yes because $S$ is a subset of $T$



Any hints/solution will be apprecaited



thanks u






abstract-algebra




abstract-algebra






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 19 at 22:24









jasmine

1,388416




1,388416








  • 4




    Check also $S$ is closed under subtraction, closed under multiplication, and it contains the multiplicative identity $1$.
    – i707107
    Nov 19 at 22:27






  • 1




    Its a subset but as said, you need to check that it is closed under addition, contains the additive inverse of each element, it is closed under multiplication and contains the unit element 1.
    – Wuestenfux
    Nov 20 at 12:09














  • 4




    Check also $S$ is closed under subtraction, closed under multiplication, and it contains the multiplicative identity $1$.
    – i707107
    Nov 19 at 22:27






  • 1




    Its a subset but as said, you need to check that it is closed under addition, contains the additive inverse of each element, it is closed under multiplication and contains the unit element 1.
    – Wuestenfux
    Nov 20 at 12:09








4




4




Check also $S$ is closed under subtraction, closed under multiplication, and it contains the multiplicative identity $1$.
– i707107
Nov 19 at 22:27




Check also $S$ is closed under subtraction, closed under multiplication, and it contains the multiplicative identity $1$.
– i707107
Nov 19 at 22:27




1




1




Its a subset but as said, you need to check that it is closed under addition, contains the additive inverse of each element, it is closed under multiplication and contains the unit element 1.
– Wuestenfux
Nov 20 at 12:09




Its a subset but as said, you need to check that it is closed under addition, contains the additive inverse of each element, it is closed under multiplication and contains the unit element 1.
– Wuestenfux
Nov 20 at 12:09















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