New Classes of Finitely Separable Finitely Generated Commutative Rings
Overview
My research aims to study the finite separability of finitely generated commutative rings. It is of interest because of its connection with the so-called algorithmic problem of entering a subring. The global solution to this problem is still unknown. My main result describes finitely separable prime quadratic extensions of monogenic rings of prime characteristic. This result is a significant advance in this topic in recent years and allows to obtain a wide class of rings in which the above problem is algorithmically solvable, and this is a non-trivial diophantine problem in the ring of polynomials with integer coefficients.
Competition history
- ISEF 2021
Resources
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Source: Regeneron International Science and Engineering Fair