关于Jacobson猜想 (3-3)

3.5. Cᴏʀᴏʟʟᴀʀʏ. Let R be α left principαl ideαl domαin with α left Moritα duαlity. Then Jω(R)＝0.

Proof.As ʀR is l.c.d.，idempotents modulo the Jacobson radical lift. Thus，since R is a domain，R must be ly now Proposition 3.4.

3.6. Remαrk. The ring R in 2.10 is a left principal ring.Thus 2.11 shows that the hypothesis “domain” in Corollary 3.5 cannot be omitied.

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