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Medial subcartesian products of fields. (English) Zbl 0702.13004
Let A (respectively B) be the direct product (respectively sum) of fields \(\{F_ i\}_{i\in J}\) with \(B\subset A\), so B is an ideal of the ring A. The authors claim to give a description of subrings R of A which contain B. One such ring is \(M=Z.1_ A+B\) with \(R\supset M\) for all R, and \(M=A\) if, and only if, J is finite (although the proof presented contains an error).
Reviewer: D.Kirby
MSC:
13B02 Extension theory of commutative rings
12E99 General field theory
13A15 Ideals and multiplicative ideal theory in commutative rings
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References:
[1] Ježek, Jaroslav: Univerzální algebra a teorie modelů. (Universal algebra and model-theory, czech original), SNTL, Praha 1976.
[2] Калужнин Л. А.: Введение в общую алгебру. Hayka, Москва 1973. · Zbl 1221.53041
[3] Ламбек, Иоахим: Кольца и модули. (English original: Lectures on rings and modules); publ. Mnp, Москва 1971. · Zbl 1170.92344 · doi:10.1016/0022-5193(71)90054-3
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