arXiv Open Access 2022

On the ideal avoidance property

Justin Chen Abolfazl Tarizadeh

Lihat Sumber

Abstrak

In this article, we investigate the avoidance property of ideals and rings. Among the main results, a general version of the avoidance lemma is formulated. It is shown that every idempotent ideal (and hence every pure ideal) has avoidance. The avoidance property of arbitrary direct products of avoidance rings is characterized. It is shown that every overring of an avoidance domain is an avoidance domain. Next, we show that every avoidance $\mathbb{N}$-graded ring whose base subring is a finite field is a PIR. It is also proved that the avoidance property is preserved under flat ring epimorphisms. Dually, we formulate a notion of strong avoidance, and show that it is reflected by pure morphisms.

Topik & Kata Kunci

math.AC math.AG

Penulis (2)

Justin Chen

Abolfazl Tarizadeh

Format Sitasi

APA MLA BibTeX

Chen, J., Tarizadeh, A. (2022). On the ideal avoidance property. https://arxiv.org/abs/2203.04256

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓