Commutative rings in which every pure ideal is projective

被引：0
|
作者：
Mahdou N. [1 ]
El Khalfaoui R. [1 ]
机构：
[1] Department of Mathematics, Faculty of Science and Technology of Fez, University S.M. Ben Abdellah Fez, Box 2202, Fez
来源：
ANNALI DELL'UNIVERSITA' DI FERRARA | 2019年 / 65卷 / 2期
关键词：
Amalgamation of rings; PIP-ring; Projective ideal; Pullback; Pure ideal; Trivial extension;
D O I：
10.1007/s11565-019-00324-3
中图分类号：
学科分类号：
摘要：
In this paper, we study the class of rings in which every pure ideal is projective. We investigate the stability of this property under homomorphic image, and its transfer to various contexts of constructions such as pullbacks trivial ring extensions and amalgamation of rings. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property. © 2019, Università degli Studi di Ferrara.
引用
收藏
页码：301 / 310
页数：9
相关论文
共 50 条
  • [31] RINGS IN WHICH EVERY MAXIMAL IDEAL IS GENERATED BY A CENTRAL IDEMPOTENT
    OSHIRO, K
    PROCEEDINGS OF THE JAPAN ACADEMY, 1970, 46 (06): : 472 - &
  • [32] ALTERNATIVE RINGS IN WHICH EVERY PROPER RIGHT IDEAL IS MAXIMAL
    WIDIGER, A
    FUNDAMENTA MATHEMATICAE, 1983, 116 (03) : 165 - 167
  • [33] RINGS IN WHICH EVERY RIGHT IDEAL IS QUASI-INJECTIVE
    JAIN, SK
    MOHAMED, SH
    SINGH, S
    PACIFIC JOURNAL OF MATHEMATICS, 1969, 31 (01) : 73 - &
  • [34] Rings in which every nonzero weakly prime ideal is prime
    Abdelhaq El Khalfi
    Najib Mahdou
    Youssef Zahir
    São Paulo Journal of Mathematical Sciences, 2020, 14 : 689 - 697
  • [35] Rings in which every nonzero weakly prime ideal is prime
    El Khalfi, Abdelhaq
    Mahdou, Najib
    Zahir, Youssef
    SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2020, 14 (02): : 689 - 697
  • [36] Rings in which every 2-absorbing ideal is prime
    Bennis D.
    Fahid B.
    Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2018, 59 (2): : 391 - 396
  • [37] RINGS IN WHICH EVERY COMPLEMENT RIGHT IDEAL IS A DIRECT SUMMAND
    CHATTERS, AW
    HAJARNAVIS, CR
    QUARTERLY JOURNAL OF MATHEMATICS, 1977, 28 (109): : 61 - 80
  • [38] ON RINGS OVER WHICH EVERY FLAT LEFT MODULE IS FINITELY PROJECTIVE
    ZHU, SG
    JOURNAL OF ALGEBRA, 1991, 139 (02) : 311 - 321
  • [39] When every finitely projective ideal is projective
    Najib Mahdou
    Sanae Moussaoui
    Moutu Abdou Salam Moutui
    Indian Journal of Pure and Applied Mathematics, 2022, 53 : 579 - 586
  • [40] Big pure projective modules over commutative noetherian rings: Comparison with the completion
    Herbera, Dolors
    Prihoda, Pavel
    Wiegand, Roger
    FORUM MATHEMATICUM, 2024,
12345