Vector subspaces of finite fields and star operations on pseudo-valuation domains
نویسندگان
چکیده
منابع مشابه
Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields
We give a de nition, in the ring language, of Zp inside Qp and of Fp[[t]] inside Fp((t)), which works uniformly for all p and all nite eld extensions of these elds, and in many other Henselian valued elds as well. The formula can be taken existential-universal in the ring language, and in fact existential in a modi cation of the language of Macintyre. Furthermore, we show the negative result th...
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Let ∗ be a star operation on an integral domain D. Let f(D) be the set of all nonzero finitely generated fractional ideals of D. Call D a ∗–Prüfer (respectively, (∗, v)–Prüfer) domain if (FF−1)∗ = D (respectively, (F vF−1)∗ = D) for all F ∈ f(D). We establish that ∗–Prüfer domains (and (∗, v)–Prüfer domains) for various star operations ∗ span a major portion of the known generalizations of Prüf...
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The aim of this paper is to generalize thenotion of pseudo-almost valuation domains to arbitrary commutative rings. It is shown that the classes of chained rings and pseudo-valuation rings are properly contained in the class of pseudo-almost valuation rings; also the class of pseudo-almost valuation rings is properly contained in the class of quasi-local rings with linearly ordere...
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Article history: Received 31 August 2011 Revised 16 December 2011 Accepted 11 April 2012 Available online 25 April 2012 Communicated by L. Storme MSC: 05B25 11T24 11T71
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2019
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2018.11.001