Real closures of commutative rings. I.
1975; De Gruyter; Volume: 1975; Issue: 274-275 Linguagem: Inglês
10.1515/crll.1975.274-275.61
ISSN1435-5345
Autores Tópico(s)Fuzzy and Soft Set Theory
ResumoA part of the results of this paper has been announced in [13].J ) In the case of fields a proof of (0.1) by the methods of this paper is already contained in [14].B' -j+ D -r^-B" ®B.D. Thus (1 ® x) °<P i s a covering of A, hence also xp B and oc: A -> C are coverings of a connected Tiring A. Then every homomorphism ß: 2?-> C with ß o cpoc is also a covering.Proof.This had been stated for oc and cp finite already in Lemma 1.1.We regard C as an overring of A and oc as the inclusion map from A to C.i) The assertion is true if (p is a finite covering.Indeed, C is the union of a directed system (C 0 i € I) of subrings containing cp(B) such that all A are finite coverings.By Lemma 1. 1 the maps B->C i induced by ß are also finite coverings.Thus ß is a covering.
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