How to solve abstract algebra questions

timer Asked: Mar 27th, 2014

Question Description

I have a doubt in this proof:


My doubt was reduced to the last paragraph, I understood that there are some g_1,g_2 such that f_1g_1 f_2g_2 has leading coefficient 1 and degree ≤d−1 but why by row operations we can suppose for some i≠1,2, f_i=f_1g_1 f_2g_2?


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