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This paper introduces a subset of the set of 1-absorbing primary ideals introduced in [3]. An ideal <italic>I</italic> of a ring <italic>R</italic> is (1,2)-absorbing primary if, whenever non-unit elements <italic>α, β, γ</italic> ∈ <italic>R</italic> with <italic>αβγ</italic> ∈ <italic>I</italic>,then <italic>αβ</italic> ∈ <italic>I</italic> or <italic>γ</italic>2 ∈ <italic>I</italic>. The introduced notion is related to uniformly primary ideals introduced in [5]. The first main objective of this paper is to compare (1,2)-absorbing primary ideals with uniformly primary ideals with order less than or equal 2, as well as to characterize them in many classes of rings. The second part of this paper characterizes, by using (1,2)-absorbing primary ideals, the rings <italic>R</italic> for which all ideals lie between N(<italic>R</italic>) (the nil-radical of <italic>R</italic>)and N(<italic>R</italic>)2.
</abstract>

This paper introduces a subset of the set of 1-absorbing primary ideals introduced in [3]. An ideal I of a ring R is (1,2)-absorbing primary if, whenever non-unit elements α, β, γ ∈ R with αβγ ∈ I,then αβ ∈ I or γ2 ∈ I. The introduced notion is related to uniformly primary ideals introduced in [5]. The first main objective of this paper is to compare (1,2)-absorbing primary ideals with uniformly primary ideals with order less than or equal 2, as well as to characterize them in many classes of rings. The second part of this paper characterizes, by using (1,2)-absorbing primary ideals, the rings R for which all ideals lie between N(R) (the nil-radical of R)and N(R)2.

On (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2

Department of Mathematics, Faculty of Sciences

Department of Mathematics and computer, Faculty Multidisciplinary of Nador

Department of Mathematics, Faculty of Science

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2"}

This paper introduces a subset of the set of 1-absorbing primary ideals introduced in [3]. An ideal I of a ring R is (1,2)-absorbing primary if, whenever...

On (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2

Published Online: Feb 04, 2023

Page range: 5 - 21

Received: May 13, 2022

Accepted: Sep 15, 2022

DOI: https://doi.org/10.2478/auom-2023-0001

Keywords
(Uniformly) primary ideals, -rings, 1-absorbing primary ideals

© 2023 Khaled Alhazmy et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2

Published Online: Feb 04, 2023

Page range: 5 - 21

Received: May 13, 2022

Accepted: Sep 15, 2022

DOI: https://doi.org/10.2478/auom-2023-0001

Keywords(Uniformly) primary ideals, -rings, 1-absorbing primary ideals

© 2023 Khaled Alhazmy et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
(Uniformly) primary ideals, -rings, 1-absorbing primary ideals