Rings and domains

[modern torrent]

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[wary falcon]

o

Laxit doesn't work?

alr

I tried directly and by contradiction but I can't find a way to move forward.

Any ideas or hints, please?

[charred sphinx]

$$a(bab)a = \ldots$$

for b)

[pliant flint]

aL

[charred sphinx]

@wary falcon

i don't see why R would be commutative

as for zero divisors

take nonzero a, then we have unique b such that aba=a

take some other element c such that ca = 0 and analyse the quantity

$$a(b+c)a$$

[pliant flint]

aL

[charred sphinx]

if you can show it's = a, then you have b=b+c by uniqueness

with no zero divisors you also get identity element in R

how is integral domain defined in your course?

you require commutativity right?

[wary falcon]

Yes, need to be a commutativity ring, and don't have zero divisors

[wary falcon]

Sorry for the delay, but thanks!

[copper raft]

@wary falcon

<:HelpIcon:1304095958283321385>| Help Reminder

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[wary falcon]

+close

[copper raft]

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[copper raft]

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