Subring $R=left{frac{m}{2^a3^b}|min mathbb{Z},a,binmathbb{N}right}$
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Show that $R=left{frac{m}{2^a3^b}|min mathbb{Z},a,binmathbb{N}right}$ is a subring of $mathbb{Q}$. Show that $frac{1}{5}notin R$. Is $mathbb{Z}$ in $R$?
I have already shown, that the product, the sum and the difference of two Elements from $R$ are in $R$.
abstract-algebra ring-theory
edited Nov 21 at 11:29
Tianlalu
2,699632
asked Nov 21 at 11:23
Arjihad
369111
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up vote
0
down vote
favorite
Show that $R=left{frac{m}{2^a3^b}|min mathbb{Z},a,binmathbb{N}right}$ is a subring of $mathbb{Q}$. Show that $frac{1}{5}notin R$. Is $mathbb{Z}$ in $R$?
I have already shown, that the product, the sum and the difference of two Elements from $R$ are in $R$.
abstract-algebra ring-theory
edited Nov 21 at 11:29
Tianlalu
2,699632
asked Nov 21 at 11:23
Arjihad
369111
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Show that $R=left{frac{m}{2^a3^b}|min mathbb{Z},a,binmathbb{N}right}$ is a subring of $mathbb{Q}$. Show that $frac{1}{5}notin R$. Is $mathbb{Z}$ in $R$?
I have already shown, that the product, the sum and the difference of two Elements from $R$ are in $R$.
abstract-algebra ring-theory
edited Nov 21 at 11:29
Tianlalu
2,699632
asked Nov 21 at 11:23
Arjihad
369111
Show that $R=left{frac{m}{2^a3^b}|min mathbb{Z},a,binmathbb{N}right}$ is a subring of $mathbb{Q}$. Show that $frac{1}{5}notin R$. Is $mathbb{Z}$ in $R$?
I have already shown, that the product, the sum and the difference of two Elements from $R$ are in $R$.
abstract-algebra ring-theory
abstract-algebra ring-theory
edited Nov 21 at 11:29
Tianlalu
2,699632
asked Nov 21 at 11:23
Arjihad
369111
edited Nov 21 at 11:29
Tianlalu
2,699632
asked Nov 21 at 11:23
Arjihad
369111
edited Nov 21 at 11:29
Tianlalu
2,699632
edited Nov 21 at 11:29
Tianlalu
2,699632
edited Nov 21 at 11:29
Tianlalu
2,699632
2,699632
asked Nov 21 at 11:23
Arjihad
369111
asked Nov 21 at 11:23
Arjihad
369111
asked Nov 21 at 11:23
Arjihad
369111
369111
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
Hint:
$$
frac{1}{5}in R
iff frac{1}{5}=frac{m}{2^a3^b}
iff {2^a3^b}= {5m}
$$
answered Nov 21 at 11:31
lhf
161k9165384
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Hint:
$$
frac{1}{5}in R
iff frac{1}{5}=frac{m}{2^a3^b}
iff {2^a3^b}= {5m}
$$
answered Nov 21 at 11:31
lhf
161k9165384
add a comment |
up vote
0
down vote
Hint:
$$
frac{1}{5}in R
iff frac{1}{5}=frac{m}{2^a3^b}
iff {2^a3^b}= {5m}
$$
answered Nov 21 at 11:31
lhf
161k9165384
add a comment |
up vote
0
down vote
up vote
0
down vote
Hint:
$$
frac{1}{5}in R
iff frac{1}{5}=frac{m}{2^a3^b}
iff {2^a3^b}= {5m}
$$
answered Nov 21 at 11:31
lhf
161k9165384
Hint:
$$
frac{1}{5}in R
iff frac{1}{5}=frac{m}{2^a3^b}
iff {2^a3^b}= {5m}
$$
answered Nov 21 at 11:31
lhf
161k9165384
answered Nov 21 at 11:31
lhf
161k9165384
answered Nov 21 at 11:31
lhf
161k9165384
answered Nov 21 at 11:31
lhf
161k9165384
161k9165384
add a comment |
add a comment |
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