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arXiv · 1803.11297

Ring extensions of length 2

Gabriel Picavet·Martine Picavet-L'Hermitte
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Abstract

We characterize extensions of commutative rings $R\subset S$ such that $R\subset T$ is minimal for each $R$-subalgebra $T$ of $S$ with $T\neq R,S$. This property is equivalent to $R\subset S$ has length 2. Such extensions are either pointwise minimal or simple. We are able to compute the number of subextensions of $R\subset S$. 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.

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Gabriel Picavet, Martine Picavet-L'Hermitte. 2018-03-30. Ring extensions of length 2. https://arxiv.org/abs/1803.11297

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