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#### Krizalid

##### Active member

- Feb 9, 2012

- 118

Hi guys, it's been a while! Here's an interesting problem.

Let $A$ be a ring and $Z$ be the ring of $\mathbb Z.$ Consider the cartesian product $A\times Z.$

Define $A\times Z$ the product $(a,n)\cdot(b,m)=(ma+nb+ab,nm).$

Let $f:A\longmapsto A\times Z$ be defined by $f(a)=(a,0)$ for all $a$ in the ring $A.$ Prove that if $J$ is an ideal of $A,$ its image below the function $f$ is an ideal of the ring $A\times Z.$

Let $A$ be a ring and $Z$ be the ring of $\mathbb Z.$ Consider the cartesian product $A\times Z.$

Define $A\times Z$ the product $(a,n)\cdot(b,m)=(ma+nb+ab,nm).$

Let $f:A\longmapsto A\times Z$ be defined by $f(a)=(a,0)$ for all $a$ in the ring $A.$ Prove that if $J$ is an ideal of $A,$ its image below the function $f$ is an ideal of the ring $A\times Z.$

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