determine $m$ such that $langle m rangle = langle 28 rangle cap langle 35 rangle$
Clash Royale CLAN TAG#URR8PPP
up vote
1
down vote
favorite
I need to find a value for $m$, thought of finding the greatest common divisor between the two numbers, but $langle rangle$ represents an ideal, don't know if that's the way to solve this problem.
I should also mention that I already know that the intersection of two ideals is also an ideal.
Help would be appreciated.
ring-theory algebraic-number-theory
edited Sep 10 at 20:45
Mr. Brooks
13811237
asked Sep 10 at 3:19
DavidTomahawk
455216
add a comment |Â
up vote
1
down vote
favorite
I need to find a value for $m$, thought of finding the greatest common divisor between the two numbers, but $langle rangle$ represents an ideal, don't know if that's the way to solve this problem.
I should also mention that I already know that the intersection of two ideals is also an ideal.
Help would be appreciated.
ring-theory algebraic-number-theory
edited Sep 10 at 20:45
Mr. Brooks
13811237
asked Sep 10 at 3:19
DavidTomahawk
455216
1
The proper TeX for ideal brackets islangle generator rangle. Which is why a lot of people on this site prefer instead to use(generator), or even a Fraktur letter, like $mathfrakG$ or $mathfrakM$.
– Mr. Brooks
Sep 10 at 20:27
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I need to find a value for $m$, thought of finding the greatest common divisor between the two numbers, but $langle rangle$ represents an ideal, don't know if that's the way to solve this problem.
I should also mention that I already know that the intersection of two ideals is also an ideal.
Help would be appreciated.
ring-theory algebraic-number-theory
edited Sep 10 at 20:45
Mr. Brooks
13811237
asked Sep 10 at 3:19
DavidTomahawk
455216
I need to find a value for $m$, thought of finding the greatest common divisor between the two numbers, but $langle rangle$ represents an ideal, don't know if that's the way to solve this problem.
I should also mention that I already know that the intersection of two ideals is also an ideal.
Help would be appreciated.
ring-theory algebraic-number-theory
ring-theory algebraic-number-theory
edited Sep 10 at 20:45
Mr. Brooks
13811237
asked Sep 10 at 3:19
DavidTomahawk
455216
edited Sep 10 at 20:45
Mr. Brooks
13811237
asked Sep 10 at 3:19
DavidTomahawk
455216
edited Sep 10 at 20:45
Mr. Brooks
13811237
edited Sep 10 at 20:45
Mr. Brooks
13811237
edited Sep 10 at 20:45
Mr. Brooks
13811237
13811237
asked Sep 10 at 3:19
DavidTomahawk
455216
asked Sep 10 at 3:19
DavidTomahawk
455216
asked Sep 10 at 3:19
DavidTomahawk
455216
455216
1
The proper TeX for ideal brackets islangle generator rangle. Which is why a lot of people on this site prefer instead to use(generator), or even a Fraktur letter, like $mathfrakG$ or $mathfrakM$.
– Mr. Brooks
Sep 10 at 20:27
add a comment |Â
1
The proper TeX for ideal brackets islangle generator rangle. Which is why a lot of people on this site prefer instead to use(generator), or even a Fraktur letter, like $mathfrakG$ or $mathfrakM$.
– Mr. Brooks
Sep 10 at 20:27
1
1
The proper TeX for ideal brackets is
langle generator rangle. Which is why a lot of people on this site prefer instead to use (generator), or even a Fraktur letter, like $mathfrakG$ or $mathfrakM$.– Mr. Brooks
Sep 10 at 20:27
The proper TeX for ideal brackets is
langle generator rangle. Which is why a lot of people on this site prefer instead to use (generator), or even a Fraktur letter, like $mathfrakG$ or $mathfrakM$.– Mr. Brooks
Sep 10 at 20:27
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
3
down vote
accepted
You want $m in langle 28 rangle cap langle 35 rangle$. So $m=28k$ and $m=35l$ for some $k,l in mathbbZ$. Thus $28k=35l implies 4k=5l$. But $gcd(4,5)=1$, therefore $4 | l$ and $5 | k$. This implies $$m=140j qquad text for some j in mathbbZ.$$
But $m$ is a generator so least positive such value is $m=140$.
answered Sep 10 at 3:42
Anurag A
22.9k12244
How come "$4 | l$ and $5 | k$" implies that value of m?
– DavidTomahawk
Sep 10 at 3:44
1
@DavidTomahawk $4 | l implies l=4j$, thus $m=35l=35(4j)=140j$.
– Anurag A
Sep 10 at 3:52
add a comment |Â
up vote
0
down vote
You want to find the least common multiple of $28$ and $35$
That is $140$ so you ideal is$$ <140> = <28> cap <35> $$
answered Sep 10 at 3:33
Mohammad Riazi-Kermani
32.2k41853
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
You want $m in langle 28 rangle cap langle 35 rangle$. So $m=28k$ and $m=35l$ for some $k,l in mathbbZ$. Thus $28k=35l implies 4k=5l$. But $gcd(4,5)=1$, therefore $4 | l$ and $5 | k$. This implies $$m=140j qquad text for some j in mathbbZ.$$
But $m$ is a generator so least positive such value is $m=140$.
answered Sep 10 at 3:42
Anurag A
22.9k12244
How come "$4 | l$ and $5 | k$" implies that value of m?
– DavidTomahawk
Sep 10 at 3:44
1
@DavidTomahawk $4 | l implies l=4j$, thus $m=35l=35(4j)=140j$.
– Anurag A
Sep 10 at 3:52
add a comment |Â
up vote
3
down vote
accepted
You want $m in langle 28 rangle cap langle 35 rangle$. So $m=28k$ and $m=35l$ for some $k,l in mathbbZ$. Thus $28k=35l implies 4k=5l$. But $gcd(4,5)=1$, therefore $4 | l$ and $5 | k$. This implies $$m=140j qquad text for some j in mathbbZ.$$
But $m$ is a generator so least positive such value is $m=140$.
answered Sep 10 at 3:42
Anurag A
22.9k12244
How come "$4 | l$ and $5 | k$" implies that value of m?
– DavidTomahawk
Sep 10 at 3:44
1
@DavidTomahawk $4 | l implies l=4j$, thus $m=35l=35(4j)=140j$.
– Anurag A
Sep 10 at 3:52
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
You want $m in langle 28 rangle cap langle 35 rangle$. So $m=28k$ and $m=35l$ for some $k,l in mathbbZ$. Thus $28k=35l implies 4k=5l$. But $gcd(4,5)=1$, therefore $4 | l$ and $5 | k$. This implies $$m=140j qquad text for some j in mathbbZ.$$
But $m$ is a generator so least positive such value is $m=140$.
answered Sep 10 at 3:42
Anurag A
22.9k12244
You want $m in langle 28 rangle cap langle 35 rangle$. So $m=28k$ and $m=35l$ for some $k,l in mathbbZ$. Thus $28k=35l implies 4k=5l$. But $gcd(4,5)=1$, therefore $4 | l$ and $5 | k$. This implies $$m=140j qquad text for some j in mathbbZ.$$
But $m$ is a generator so least positive such value is $m=140$.
answered Sep 10 at 3:42
Anurag A
22.9k12244
answered Sep 10 at 3:42
Anurag A
22.9k12244
answered Sep 10 at 3:42
Anurag A
22.9k12244
answered Sep 10 at 3:42
Anurag A
22.9k12244
22.9k12244
How come "$4 | l$ and $5 | k$" implies that value of m?
– DavidTomahawk
Sep 10 at 3:44
1
@DavidTomahawk $4 | l implies l=4j$, thus $m=35l=35(4j)=140j$.
– Anurag A
Sep 10 at 3:52
add a comment |Â
How come "$4 | l$ and $5 | k$" implies that value of m?
– DavidTomahawk
Sep 10 at 3:44
1
@DavidTomahawk $4 | l implies l=4j$, thus $m=35l=35(4j)=140j$.
– Anurag A
Sep 10 at 3:52
How come "$4 | l$ and $5 | k$" implies that value of m?
– DavidTomahawk
Sep 10 at 3:44
How come "$4 | l$ and $5 | k$" implies that value of m?
– DavidTomahawk
Sep 10 at 3:44
1
1
@DavidTomahawk $4 | l implies l=4j$, thus $m=35l=35(4j)=140j$.
– Anurag A
Sep 10 at 3:52
@DavidTomahawk $4 | l implies l=4j$, thus $m=35l=35(4j)=140j$.
– Anurag A
Sep 10 at 3:52
add a comment |Â
up vote
0
down vote
You want to find the least common multiple of $28$ and $35$
That is $140$ so you ideal is$$ <140> = <28> cap <35> $$
answered Sep 10 at 3:33
Mohammad Riazi-Kermani
32.2k41853
add a comment |Â
up vote
0
down vote
You want to find the least common multiple of $28$ and $35$
That is $140$ so you ideal is$$ <140> = <28> cap <35> $$
answered Sep 10 at 3:33
Mohammad Riazi-Kermani
32.2k41853
add a comment |Â
up vote
0
down vote
up vote
0
down vote
You want to find the least common multiple of $28$ and $35$
That is $140$ so you ideal is$$ <140> = <28> cap <35> $$
answered Sep 10 at 3:33
Mohammad Riazi-Kermani
32.2k41853
You want to find the least common multiple of $28$ and $35$
That is $140$ so you ideal is$$ <140> = <28> cap <35> $$
answered Sep 10 at 3:33
Mohammad Riazi-Kermani
32.2k41853
answered Sep 10 at 3:33
Mohammad Riazi-Kermani
32.2k41853
answered Sep 10 at 3:33
Mohammad Riazi-Kermani
32.2k41853
answered Sep 10 at 3:33
Mohammad Riazi-Kermani
32.2k41853
32.2k41853
add a comment |Â
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2911459%2fdetermine-m-such-that-langle-m-rangle-langle-28-rangle-cap-langle-35%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
1
The proper TeX for ideal brackets is
langle generator rangle. Which is why a lot of people on this site prefer instead to use(generator), or even a Fraktur letter, like $mathfrakG$ or $mathfrakM$.– Mr. Brooks
Sep 10 at 20:27