## 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

### Keywords:

direct products of fields; subrings
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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
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