Mixing
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
asked 2 days ago
jasmine
1,304416
add a comment |
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
asked 2 days ago
jasmine
1,304416
4
Check also $S$ is closed under subtraction, closed under multiplication, and it contains the multiplicative identity $1$.
– i707107
2 days ago
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
2 days ago
add a comment |
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
asked 2 days ago
jasmine
1,304416
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
asked 2 days ago
jasmine
1,304416
asked 2 days ago
jasmine
1,304416
asked 2 days ago
jasmine
1,304416
asked 2 days ago
jasmine
1,304416
asked 2 days ago
jasmine
1,304416
1,304416
4
Check also $S$ is closed under subtraction, closed under multiplication, and it contains the multiplicative identity $1$.
– i707107
2 days ago
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
2 days ago
add a comment |
4
Check also $S$ is closed under subtraction, closed under multiplication, and it contains the multiplicative identity $1$.
– i707107
2 days ago
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
2 days ago
4
4
Check also $S$ is closed under subtraction, closed under multiplication, and it contains the multiplicative identity $1$.
– i707107
2 days ago
Check also $S$ is closed under subtraction, closed under multiplication, and it contains the multiplicative identity $1$.
– i707107
2 days ago
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
2 days ago
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
2 days ago
add a comment |
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4
Check also $S$ is closed under subtraction, closed under multiplication, and it contains the multiplicative identity $1$.
– i707107
2 days ago
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
2 days ago