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On ternary semifields

Tapan K. Dutta, Sukhendu Kar (2004)

Discussiones Mathematicae - General Algebra and Applications

In this paper, we introduce the notion of ternary semi-integral domain and ternary semifield and study some of their properties.In particular we also investigate the maximal ideals of the ternary semiring Z¯₀.

On the closed subfields of [...] Q ¯   p Q ¯ ˜ p

Sever Achimescu, Victor Alexandru, Corneliu Stelian Andronescu (2016)

Open Mathematics

Let p be a prime number, and let [...] Q¯ p Q ¯ ˜ 𝐩 be the completion of Q with respect to the pseudovaluation w which extends the p-adic valuation vp. In this paper our goal is to give a characterization of closed subfields of [...] Q¯ p Q ¯ ˜ 𝐩 , the completion of Q with respect w, i.e. the spectral extension of the p-adic valuation vp on Q.

On the compositum of all degree d extensions of a number field

Itamar Gal, Robert Grizzard (2014)

Journal de Théorie des Nombres de Bordeaux

We study the compositum k [ d ] of all degree d extensions of a number field k in a fixed algebraic closure. We show k [ d ] contains all subextensions of degree less than d if and only if d 4 . We prove that for d > 2 there is no bound c = c ( d ) on the degree of elements required to generate finite subextensions of k [ d ] / k . Restricting to Galois subextensions, we prove such a bound does not exist under certain conditions on divisors of d , but that one can take c = d when d is prime. This question was inspired by work of Bombieri and...

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