I'm wanting to show that given an ED R whose identity is 1, and two elements a,b∈R whose gcd is a unit, that ∃x,y∈R st ax+by=1. Caveat-- I don't want to utilize the notion of a PID, or of ideals at all directly. Any hints on how to do this?
I'm wanting to show that given an ED R whose identity is 1, and two elements a,b∈R whose gcd is a unit, that ∃x,y∈R st ax+by=1. Caveat-- I don't want to utilize the notion of a PID, or of ideals at all directly. Any hints on how to do this?
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