HIGHLIGHTS
SUMMARY
Gilmer claims he proves that C ⇒ J. This implication is also reported in D. D. Anderson`s survey. (4) A subset S of a rng R is a saturated multiplicatively closed subset of R if, for every r, r′ ∈ R, rr′ ∈ S ⇔ r ∈ S and r′ ∈ S. If rx + zx ∈ S, then (rx + zx)2 ∈ S because S is multiplicatively closed. But (rx + zx)2=(r2 x + 2zrx + z 2 x)x, and in this last product, both factors are in R. Since S is saturated in R, it follows that x ∈ S, which . . .
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