On wsq-primary ideals

Emel Aslankarayiğit Uğurlu; El Mehdi Bouba; Ünsal Tekir; Suat Koç

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 2, page 415-429
  • ISSN: 0011-4642

Abstract

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We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let R be a commutative ring with a nonzero identity and Q a proper ideal of R . The proper ideal Q is said to be a weakly strongly quasi-primary ideal if whenever 0 ≠ a b ∈ Q for some a , b ∈ R , then a 2 ∈ Q or b ∈ Q . Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero dimensional rings over which every proper ideal is wsq-primary. Finally, we study finite union of wsq-primary ideals.

How to cite

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Aslankarayiğit Uğurlu, Emel, et al. "On wsq-primary ideals." Czechoslovak Mathematical Journal 73.2 (2023): 415-429. <http://eudml.org/doc/299457>.

@article{AslankarayiğitUğurlu2023,
abstract = {We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity and $Q$ a proper ideal of $R$. The proper ideal $Q$ is said to be a weakly strongly quasi-primary ideal if whenever $0\ne ab\in Q$ for some $a,b\in R$, then $a^\{2\}\in Q$ or $b\in \sqrt\{Q\}.$ Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero dimensional rings over which every proper ideal is wsq-primary. Finally, we study finite union of wsq-primary ideals.},
author = {Aslankarayiğit Uğurlu, Emel, Bouba, El Mehdi, Tekir, Ünsal, Koç, Suat},
journal = {Czechoslovak Mathematical Journal},
keywords = {primary ideal; weakly primary ideal; quasi-primary ideal; weakly 2-prime ideal; strongly quasi-primary ideal},
language = {eng},
number = {2},
pages = {415-429},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On wsq-primary ideals},
url = {http://eudml.org/doc/299457},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Aslankarayiğit Uğurlu, Emel
AU - Bouba, El Mehdi
AU - Tekir, Ünsal
AU - Koç, Suat
TI - On wsq-primary ideals
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 2
SP - 415
EP - 429
AB - We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity and $Q$ a proper ideal of $R$. The proper ideal $Q$ is said to be a weakly strongly quasi-primary ideal if whenever $0\ne ab\in Q$ for some $a,b\in R$, then $a^{2}\in Q$ or $b\in \sqrt{Q}.$ Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero dimensional rings over which every proper ideal is wsq-primary. Finally, we study finite union of wsq-primary ideals.
LA - eng
KW - primary ideal; weakly primary ideal; quasi-primary ideal; weakly 2-prime ideal; strongly quasi-primary ideal
UR - http://eudml.org/doc/299457
ER -

References

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