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I am reading The Basics of Abstract Algebra by Paul E. Bland ...
I am focused on Section 7.2 Euclidean, Principal Ideal, Unique Factorization Domains ... ...
I need help with the proof of Theorem 7.2.14 ... ... Theorem 7.2.14 and its proof reads as follows:
View attachment 8275In the above proof by Bland we read the following:
"... ... But then $$a = apx' + aby' $$, so $$p|apx'$$ and $$p|aby'$$. ... ... "Can someone please explain exactly how/why $$p|aby'$$... ... ?
Peter
I am focused on Section 7.2 Euclidean, Principal Ideal, Unique Factorization Domains ... ...
I need help with the proof of Theorem 7.2.14 ... ... Theorem 7.2.14 and its proof reads as follows:
View attachment 8275In the above proof by Bland we read the following:
"... ... But then $$a = apx' + aby' $$, so $$p|apx'$$ and $$p|aby'$$. ... ... "Can someone please explain exactly how/why $$p|aby'$$... ... ?
Peter