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I am reading The Basics of Abstract Algebra by Paul E. Bland ...
I am focused on Section 3.2 Subrings, Ideals and Factor Rings ... ...
I need help with another aspect of the proof of Theorem 3.2.19 ... ... Theorem 3.2.19 and its proof reads as follows:
https://www.physicsforums.com/attachments/8270
In the above proof by Bland we read the following:"... ... Hence $$x = you =yxb$$ which implies that $$yb = e$$ ... ...
Can someone please explain exactly how/why $$x = you =yxb$$ implies that $$yb = e$$ ... ...
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***EDIT***
Is it simply because $$x = yxb = xyb$$ since R is commutative and then
$$x = xyb \Longrightarrow yb = e$$ ... is that correct?
But how do we know $$x \neq 0$$ ...------------------------------------------------------------------------------------------------------
Peter
I am focused on Section 3.2 Subrings, Ideals and Factor Rings ... ...
I need help with another aspect of the proof of Theorem 3.2.19 ... ... Theorem 3.2.19 and its proof reads as follows:
https://www.physicsforums.com/attachments/8270
In the above proof by Bland we read the following:"... ... Hence $$x = you =yxb$$ which implies that $$yb = e$$ ... ...
Can someone please explain exactly how/why $$x = you =yxb$$ implies that $$yb = e$$ ... ...
------------------------------------------------------------------------------------------------------
***EDIT***
Is it simply because $$x = yxb = xyb$$ since R is commutative and then
$$x = xyb \Longrightarrow yb = e$$ ... is that correct?
But how do we know $$x \neq 0$$ ...------------------------------------------------------------------------------------------------------
Peter
Last edited: