A note on the Galois correspondence for commutative rings (Q1921910)

The Galois correspondence for commutative rings from the third author's book ``The separable Galois theory of commutative rings'' [New York: Dekker (1974; Zbl 0284.13004)] is not correct, as it is shown here. This note gives the correct correspondence using the general Galois theory from the second author's papers [Soobshch. Akad. Nauk Gruz. SSR 114, 497-500 (1984; Zbl 0558.18001), Math. USSR Sb. 64, No. 2, 359-374 (1989); translation from Mat. Sb., Nov. Ser. 136(178), Nr. 3(7), 361-376 (1988; Zbl 0653.18002); J. Algebra 132, No. 2, 270-286 (1990; Zbl 0702.18006)].