# The definition of 'reducible' in Hungerford's Algebra text

1. Mar 27, 2012

### julypraise

He starts using the term 'reducible', as it came out of nowhere, from the page 162 of the text.

I know, roughly, what kind of thing he mean by this 'reducible' obejct. (That is that an element is factored into two elements that are not units.) And this should not be a problem if this term is used in only a informal essay type discussion level. But then, on the page 164, he uses this term in the proof (thm 6.13). And also, the page 273, the proof of the prop 4.11: 'f is either irreducible or reducible', which kinda suggests that 'reducible' means 'not irreducible'. Also page 274, on the top and the bottom both.

This is a problem for me.

If I take 'reducible' as 'not reducible' then 0 and units are reducible too, which may be a problem. But it maybe not at least in this text.

So is this interpretation safe in this text?

2. Mar 27, 2012

### morphism

In all those instances he's referring to a polynomial, where the adjective "reducible" has its usual meaning.

I guess generally one would call a nonzero nonunit reducible if it isn't irreducible - equivalently, if you could write it as a product of two nonzero nonunits.

3. Mar 27, 2012

### julypraise

Okay, I will take note of that.