Mixing
Subring $R=left{frac{m}{2^a3^b}|min mathbb{Z},a,binmathbb{N}right}$
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 '18 at 11:29
Tianlalu
3,09621038
asked Nov 21 '18 at 11:23
Arjihad
383111
add a comment |
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 '18 at 11:29
Tianlalu
3,09621038
asked Nov 21 '18 at 11:23
Arjihad
383111
add a comment |
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 '18 at 11:29
Tianlalu
3,09621038
asked Nov 21 '18 at 11:23
Arjihad
383111
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 '18 at 11:29
Tianlalu
3,09621038
asked Nov 21 '18 at 11:23
Arjihad
383111
edited Nov 21 '18 at 11:29
Tianlalu
3,09621038
asked Nov 21 '18 at 11:23
Arjihad
383111
edited Nov 21 '18 at 11:29
Tianlalu
3,09621038
edited Nov 21 '18 at 11:29
Tianlalu
3,09621038
edited Nov 21 '18 at 11:29
Tianlalu
3,09621038
3,09621038
asked Nov 21 '18 at 11:23
Arjihad
383111
asked Nov 21 '18 at 11:23
Arjihad
383111
asked Nov 21 '18 at 11:23
Arjihad
383111
383111
add a comment |
add a comment |
1 Answer
1
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oldest
votes
Hint:
$$
frac{1}{5}in R
iff frac{1}{5}=frac{m}{2^a3^b}
iff {2^a3^b}= {5m}
$$
answered Nov 21 '18 at 11:31
lhf
163k10167387
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Hint:
$$
frac{1}{5}in R
iff frac{1}{5}=frac{m}{2^a3^b}
iff {2^a3^b}= {5m}
$$
answered Nov 21 '18 at 11:31
lhf
163k10167387
add a comment |
Hint:
$$
frac{1}{5}in R
iff frac{1}{5}=frac{m}{2^a3^b}
iff {2^a3^b}= {5m}
$$
answered Nov 21 '18 at 11:31
lhf
163k10167387
add a comment |
Hint:
$$
frac{1}{5}in R
iff frac{1}{5}=frac{m}{2^a3^b}
iff {2^a3^b}= {5m}
$$
answered Nov 21 '18 at 11:31
lhf
163k10167387
Hint:
$$
frac{1}{5}in R
iff frac{1}{5}=frac{m}{2^a3^b}
iff {2^a3^b}= {5m}
$$
answered Nov 21 '18 at 11:31
lhf
163k10167387
answered Nov 21 '18 at 11:31
lhf
163k10167387
answered Nov 21 '18 at 11:31
lhf
163k10167387
answered Nov 21 '18 at 11:31
lhf
163k10167387
163k10167387
add a comment |
add a comment |
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