Prime element in Integer [closed]
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In book definition of prime element in integral domain is, A non-zero non unit a∈R is said to be prime element if a|bc then a|b or a|c. As Z is an integral domain as 4|4.1 and 4|4 that means 4 is prime element but 4 is not prime in Z.
ring-theory
asked Nov 24 at 7:01
user499117
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closed as unclear what you're asking by Morgan Rodgers, Gibbs, Joel Reyes Noche, Batominovski, José Carlos Santos Nov 24 at 14:07
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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In book definition of prime element in integral domain is, A non-zero non unit a∈R is said to be prime element if a|bc then a|b or a|c. As Z is an integral domain as 4|4.1 and 4|4 that means 4 is prime element but 4 is not prime in Z.
ring-theory
asked Nov 24 at 7:01
user499117
389
closed as unclear what you're asking by Morgan Rodgers, Gibbs, Joel Reyes Noche, Batominovski, José Carlos Santos Nov 24 at 14:07
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
2
$4mid(2times2)$.
– Lord Shark the Unknown
Nov 24 at 7:05
Please see math.meta.stackexchange.com/questions/5020/…
– Lord Shark the Unknown
Nov 24 at 7:05
1
Is there a question here?
– Morgan Rodgers
Nov 24 at 7:12
1
Not for a single case. For all cases. It doesn't matter if there is some pair of $b,c$ where this is true. It must be true for all pairs. So,yes, it is true for $a=4; b=4; c=1$ but that's not good enough. It is not true for $a = 4; b =2; c=2$. And so $4$ is not prime.
– fleablood
Nov 24 at 7:12
@fleablood ok thank you sir... In Set of real number Is every element is irreducible? This quation not related to above quation.but i have dout so i ask.
– user499117
Nov 24 at 7:19
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show 3 more comments
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
In book definition of prime element in integral domain is, A non-zero non unit a∈R is said to be prime element if a|bc then a|b or a|c. As Z is an integral domain as 4|4.1 and 4|4 that means 4 is prime element but 4 is not prime in Z.
ring-theory
asked Nov 24 at 7:01
user499117
389
In book definition of prime element in integral domain is, A non-zero non unit a∈R is said to be prime element if a|bc then a|b or a|c. As Z is an integral domain as 4|4.1 and 4|4 that means 4 is prime element but 4 is not prime in Z.
ring-theory
ring-theory
asked Nov 24 at 7:01
user499117
389
asked Nov 24 at 7:01
user499117
389
asked Nov 24 at 7:01
user499117
389
asked Nov 24 at 7:01
user499117
389
asked Nov 24 at 7:01
user499117
389
389
closed as unclear what you're asking by Morgan Rodgers, Gibbs, Joel Reyes Noche, Batominovski, José Carlos Santos Nov 24 at 14:07
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Morgan Rodgers, Gibbs, Joel Reyes Noche, Batominovski, José Carlos Santos Nov 24 at 14:07
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
2
$4mid(2times2)$.
– Lord Shark the Unknown
Nov 24 at 7:05
Please see math.meta.stackexchange.com/questions/5020/…
– Lord Shark the Unknown
Nov 24 at 7:05
1
Is there a question here?
– Morgan Rodgers
Nov 24 at 7:12
1
Not for a single case. For all cases. It doesn't matter if there is some pair of $b,c$ where this is true. It must be true for all pairs. So,yes, it is true for $a=4; b=4; c=1$ but that's not good enough. It is not true for $a = 4; b =2; c=2$. And so $4$ is not prime.
– fleablood
Nov 24 at 7:12
@fleablood ok thank you sir... In Set of real number Is every element is irreducible? This quation not related to above quation.but i have dout so i ask.
– user499117
Nov 24 at 7:19
|
show 3 more comments
2
$4mid(2times2)$.
– Lord Shark the Unknown
Nov 24 at 7:05
Please see math.meta.stackexchange.com/questions/5020/…
– Lord Shark the Unknown
Nov 24 at 7:05
1
Is there a question here?
– Morgan Rodgers
Nov 24 at 7:12
1
Not for a single case. For all cases. It doesn't matter if there is some pair of $b,c$ where this is true. It must be true for all pairs. So,yes, it is true for $a=4; b=4; c=1$ but that's not good enough. It is not true for $a = 4; b =2; c=2$. And so $4$ is not prime.
– fleablood
Nov 24 at 7:12
@fleablood ok thank you sir... In Set of real number Is every element is irreducible? This quation not related to above quation.but i have dout so i ask.
– user499117
Nov 24 at 7:19
2
2
$4mid(2times2)$.
– Lord Shark the Unknown
Nov 24 at 7:05
$4mid(2times2)$.
– Lord Shark the Unknown
Nov 24 at 7:05
Please see math.meta.stackexchange.com/questions/5020/…
– Lord Shark the Unknown
Nov 24 at 7:05
Please see math.meta.stackexchange.com/questions/5020/…
– Lord Shark the Unknown
Nov 24 at 7:05
1
1
Is there a question here?
– Morgan Rodgers
Nov 24 at 7:12
Is there a question here?
– Morgan Rodgers
Nov 24 at 7:12
1
1
Not for a single case. For all cases. It doesn't matter if there is some pair of $b,c$ where this is true. It must be true for all pairs. So,yes, it is true for $a=4; b=4; c=1$ but that's not good enough. It is not true for $a = 4; b =2; c=2$. And so $4$ is not prime.
– fleablood
Nov 24 at 7:12
Not for a single case. For all cases. It doesn't matter if there is some pair of $b,c$ where this is true. It must be true for all pairs. So,yes, it is true for $a=4; b=4; c=1$ but that's not good enough. It is not true for $a = 4; b =2; c=2$. And so $4$ is not prime.
– fleablood
Nov 24 at 7:12
@fleablood ok thank you sir... In Set of real number Is every element is irreducible? This quation not related to above quation.but i have dout so i ask.
– user499117
Nov 24 at 7:19
@fleablood ok thank you sir... In Set of real number Is every element is irreducible? This quation not related to above quation.but i have dout so i ask.
– user499117
Nov 24 at 7:19
|
show 3 more comments
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2
$4mid(2times2)$.
– Lord Shark the Unknown
Nov 24 at 7:05
Please see math.meta.stackexchange.com/questions/5020/…
– Lord Shark the Unknown
Nov 24 at 7:05
1
Is there a question here?
– Morgan Rodgers
Nov 24 at 7:12
1
Not for a single case. For all cases. It doesn't matter if there is some pair of $b,c$ where this is true. It must be true for all pairs. So,yes, it is true for $a=4; b=4; c=1$ but that's not good enough. It is not true for $a = 4; b =2; c=2$. And so $4$ is not prime.
– fleablood
Nov 24 at 7:12
@fleablood ok thank you sir... In Set of real number Is every element is irreducible? This quation not related to above quation.but i have dout so i ask.
– user499117
Nov 24 at 7:19