Invariant basis number for Rings.
$begingroup$
Let $R$ be a ring with identity. Let $M_{n}(R)$ be the ring of $n$ by $n$ matrices with entries in $R$. Prove that $R$ has IBN iff $M_{n}(R)$ has IBN.
I was given this problem. I thought a little about that and came out with nothing special. So if you could give some hint on that, it would be great.
abstract-algebra ring-theory modules
asked Dec 7 '18 at 16:24
AmirhosseinAmirhossein
616
$endgroup$
add a comment |
$begingroup$
Let $R$ be a ring with identity. Let $M_{n}(R)$ be the ring of $n$ by $n$ matrices with entries in $R$. Prove that $R$ has IBN iff $M_{n}(R)$ has IBN.
I was given this problem. I thought a little about that and came out with nothing special. So if you could give some hint on that, it would be great.
abstract-algebra ring-theory modules
asked Dec 7 '18 at 16:24
AmirhosseinAmirhossein
616
$endgroup$
$begingroup$
Have a look on exercises in modules and rings, e.g. here (Exercise $1.14$).
$endgroup$
– Dietrich Burde
Dec 7 '18 at 16:41
add a comment |
$begingroup$
Let $R$ be a ring with identity. Let $M_{n}(R)$ be the ring of $n$ by $n$ matrices with entries in $R$. Prove that $R$ has IBN iff $M_{n}(R)$ has IBN.
I was given this problem. I thought a little about that and came out with nothing special. So if you could give some hint on that, it would be great.
abstract-algebra ring-theory modules
asked Dec 7 '18 at 16:24
AmirhosseinAmirhossein
616
$endgroup$
Let $R$ be a ring with identity. Let $M_{n}(R)$ be the ring of $n$ by $n$ matrices with entries in $R$. Prove that $R$ has IBN iff $M_{n}(R)$ has IBN.
I was given this problem. I thought a little about that and came out with nothing special. So if you could give some hint on that, it would be great.
abstract-algebra ring-theory modules
abstract-algebra ring-theory modules
asked Dec 7 '18 at 16:24
AmirhosseinAmirhossein
616
asked Dec 7 '18 at 16:24
AmirhosseinAmirhossein
616
asked Dec 7 '18 at 16:24
AmirhosseinAmirhossein
616
asked Dec 7 '18 at 16:24
AmirhosseinAmirhossein
616
asked Dec 7 '18 at 16:24
AmirhosseinAmirhossein
616
616
$begingroup$
Have a look on exercises in modules and rings, e.g. here (Exercise $1.14$).
$endgroup$
– Dietrich Burde
Dec 7 '18 at 16:41
add a comment |
$begingroup$
Have a look on exercises in modules and rings, e.g. here (Exercise $1.14$).
$endgroup$
– Dietrich Burde
Dec 7 '18 at 16:41
$begingroup$
Have a look on exercises in modules and rings, e.g. here (Exercise $1.14$).
$endgroup$
– Dietrich Burde
Dec 7 '18 at 16:41
$begingroup$
Have a look on exercises in modules and rings, e.g. here (Exercise $1.14$).
$endgroup$
– Dietrich Burde
Dec 7 '18 at 16:41
add a comment |
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$begingroup$
Have a look on exercises in modules and rings, e.g. here (Exercise $1.14$).
$endgroup$
– Dietrich Burde
Dec 7 '18 at 16:41