Proving that a ring with some properties is commutativeDoes there exist an ordered ring, with $mathbbZ$ as an ordered subring, such that some ring of p-adic integers can be formed as a quotient ring?A ring with prime characteristicFinite commutative ring with more than $frac23$ of its elements idempotentProving that there only finitely many minimal prime ideals of any ideal in Noetherian commutative ring$R$ be a commutative ring with unity , $|R^times|=p$ an odd prime then is $R$ isomorphic to a quotient of $mathbb Z_2[x]/langle x^p-1rangle$?A finite non commutative ring of a specific cardinalProving $a+a =0$ for Boolean ringnumber of solutions of $x^2=x$ divides the number of invertible elements in a ringShow that $2$ is invertible in a ring with odd cardinality.
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Proving that a ring with some properties is commutative
Does there exist an ordered ring, with $mathbbZ$ as an ordered subring, such that some ring of p-adic integers can be formed as a quotient ring?A ring with prime characteristicFinite commutative ring with more than $frac23$ of its elements idempotentProving that there only finitely many minimal prime ideals of any ideal in Noetherian commutative ring$R$ be a commutative ring with unity , $|R^times|=p$ an odd prime then is $R$ isomorphic to a quotient of $mathbb Z_2[x]/langle x^p-1rangle$?A finite non commutative ring of a specific cardinalProving $a+a =0$ for Boolean ringnumber of solutions of $x^2=x$ divides the number of invertible elements in a ringShow that $2$ is invertible in a ring with odd cardinality.
$begingroup$
A is a ring with the next properties:
a) the order of $1$ is p (prime) in the group $(A,+)$
b) there exists $B subset A$ with $p$ elements such that : for all $x,y in A$, exists $b in B$ which verifies $xy=byx$.
Prove that A is commutative. Can somebody give me some tips, pelase? I have no idea how to solve it.
I managed to get that $k cdot1$ is invertible for all $kin 1,2,...,p-1 $
abstract-algebra ring-theory characteristics
asked Mar 10 at 20:18
GaboruGaboru
4407
$endgroup$
add a comment |
$begingroup$
A is a ring with the next properties:
a) the order of $1$ is p (prime) in the group $(A,+)$
b) there exists $B subset A$ with $p$ elements such that : for all $x,y in A$, exists $b in B$ which verifies $xy=byx$.
Prove that A is commutative. Can somebody give me some tips, pelase? I have no idea how to solve it.
I managed to get that $k cdot1$ is invertible for all $kin 1,2,...,p-1 $
abstract-algebra ring-theory characteristics
asked Mar 10 at 20:18
GaboruGaboru
4407
$endgroup$
add a comment |
$begingroup$
A is a ring with the next properties:
a) the order of $1$ is p (prime) in the group $(A,+)$
b) there exists $B subset A$ with $p$ elements such that : for all $x,y in A$, exists $b in B$ which verifies $xy=byx$.
Prove that A is commutative. Can somebody give me some tips, pelase? I have no idea how to solve it.
I managed to get that $k cdot1$ is invertible for all $kin 1,2,...,p-1 $
abstract-algebra ring-theory characteristics
asked Mar 10 at 20:18
GaboruGaboru
4407
$endgroup$
A is a ring with the next properties:
a) the order of $1$ is p (prime) in the group $(A,+)$
b) there exists $B subset A$ with $p$ elements such that : for all $x,y in A$, exists $b in B$ which verifies $xy=byx$.
Prove that A is commutative. Can somebody give me some tips, pelase? I have no idea how to solve it.
I managed to get that $k cdot1$ is invertible for all $kin 1,2,...,p-1 $
abstract-algebra ring-theory characteristics
abstract-algebra ring-theory characteristics
asked Mar 10 at 20:18
GaboruGaboru
4407
asked Mar 10 at 20:18
GaboruGaboru
4407
asked Mar 10 at 20:18
GaboruGaboru
4407
asked Mar 10 at 20:18
GaboruGaboru
4407
asked Mar 10 at 20:18
GaboruGaboru
4407
4407
add a comment |
add a comment |
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