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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 the proof of Theorem 3.2.19 ... ... Theorem 3.2.19 and its proof reads as follows:
View attachment 8269In the above proof by Bland we read the following:"... ... If $$y \in xR$$ it immediately follows that $$xR = yR$$ ... ... Can someone please explain exactly why $$y \in xR$$ implies that $$xR = yR$$ ... ... Peter
I am focused on Section 3.2 Subrings, Ideals and Factor Rings ... ...
I need help with the proof of Theorem 3.2.19 ... ... Theorem 3.2.19 and its proof reads as follows:
View attachment 8269In the above proof by Bland we read the following:"... ... If $$y \in xR$$ it immediately follows that $$xR = yR$$ ... ... Can someone please explain exactly why $$y \in xR$$ implies that $$xR = yR$$ ... ... Peter