2018/03/30 by Gabriel Pıcavet, Picavet, Gabriel, Martine Picavet-L’Hermitte +1
Computer Science · Mathematics · #13B02 #Coding theory and cryptography #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1803.11297
openalex publication_date 2018/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize extensions of commutative rings R⊂ S such that R⊂ T is minimal for each R-subalgebra T of S with T≠ R,S. This property is equivalent to R⊂ S has length 2. Such extensions are either pointwise minimal or simple. We are able to compute the number of subextensions of R⊂ S. Besides commutative algebra considerations, our main result is a consequence of the recently introduced by van Hoeij et al. concept of principal subfields of a finite separable field extension. As a corollary of this paper, we get that simple extensions of length 2 have FIP.