On Nilcompactifications of Prime Spectra of Commutative Rings
Lorenzo Acosta G. (1), I. Marcela Rubio P. (1) ((1) Universidad, Nacional de Colombia, Bogot\'a, Colombia)
TL;DR
This paper introduces a new algebraic method called R-nilcompactification to compactify the prime spectrum of a proper ideal in a commutative ring, and explores its categorical properties.
Contribution
It presents the first algebraic construction for compactifying prime spectra of ideals in rings and analyzes its categorical features.
Findings
Provides a new algebraic compactification method for prime spectra.
Establishes categorical properties of the R-nilcompactification.
Enhances understanding of prime spectrum structures in commutative algebra.
Abstract
Given a ring R and S one of its proper ideals, we obtain a compactification of the prime spectrum of S through a mainly algebraic process. We name it the R-nilcompactification of SpecS. We study some categorical properties of this construction.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Algebraic structures and combinatorial models