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BOUNDS FOR INDEXES OF NILPOTENCY IN COMMUTATIVE RING THEORY: A PROOF MINING APPROACH

Published online by Cambridge University Press:  05 January 2021

FERNANDO FERREIRA*
Affiliation:
DEPARTAMENTO DE MATEMÁTICA FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA CAMPO GRANDE, ED. C6, 1749-016LISBOA, PORTUGAL E-mail: [email protected]

Abstract

It is well-known that an element of a commutative ring with identity is nilpotent if, and only if , it lies in every prime ideal of the ring. A modification of this fact is amenable to a very simple proof mining analysis. We formulate a quantitative version of this modification and obtain an explicit bound. We present an application. This proof mining analysis is the leitmotif for some comments and observations on the methodology of computational extraction. In particular, we emphasize that the formulation of quantitative versions of ordinary mathematical theorems is of independent interest from proof mining metatheorems.

Type
Communication
Copyright
© The Association for Symbolic Logic 2021

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References

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