Journal of Commutative Algebra

When is a Nakayama closure semiprime?

Janet C. Vassilev

Full-text: Open access

Abstract

Many well-known closure operations such as integral closure and tight closure are both semiprime operations and Nakayama closures. In this short note, we begin the study on the overlap between Nakayama closures and semiprime operations. We exhibit examples of closure operations which are either semiprime or Nakayama but not the other. In the case of a discrete valuation ring we show that a closure operation $c$ is Nakayama if and only if it is semiprime and \[ (0)^c=\bigcap_{n \geq 1} (I^n)^c \] for any ideal $I$.

Article information

Source
J. Commut. Algebra, Volume 6, Number 3 (2014), 439-454.

Dates
First available in Project Euclid: 17 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.jca/1416233326

Digital Object Identifier
doi:10.1216/JCA-2014-6-3-439

Mathematical Reviews number (MathSciNet)
MR3278812

Zentralblatt MATH identifier
1326.13001

Subjects
Primary: 13A15: Ideals; multiplicative ideal theory 13C05: Structure, classification theorems

Keywords
Closure operation semiprime op eration Nakayama closure

Citation

Vassilev, Janet C. When is a Nakayama closure semiprime?. J. Commut. Algebra 6 (2014), no. 3, 439--454. doi:10.1216/JCA-2014-6-3-439. https://projecteuclid.org/euclid.jca/1416233326


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