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In this paper we analyze strongly 2-absorbing prime ideals (shortly strongly 2-API), strongly 2-absorbing weak prime ideals (shortly strongly 2-AWPI) and 2-absorbing weak prime ideals (shortly 2-AWPI) in a non-commutative ring, which represent generalization of prime ideals (shortly PI) in a non-commutative ring. The relationship between the strongly 2-API and the 2-absorbing prime ideal (shortly 2-API) is examined. We provide examples to illustrate the new concept of strongly <italic>m</italic>a1-system and strongly <italic>m</italic>a2-system as well as the relationships beween them. Let <italic>I</italic> be an ideal of <italic>𝒭</italic> and <italic>𝒨</italic> be a strongly <italic>m</italic>a1-system such that <italic>I ∩ 𝒨</italic> = ϕ. Then there exists a strongly 2-API <italic>𝒫</italic> of <italic>𝒭</italic> containing <italic>I</italic> such that <italic>𝒫 ∩ 𝒨</italic> = ϕ. We prove that <italic>𝒫</italic> is a strongly 2-API if and only if <italic>𝒜</italic>1<italic>𝒜</italic>2<italic>𝒜</italic>3 ⊆ <italic>𝒫</italic> implies that <italic>𝒜</italic>1 ⊆ <italic>𝒫</italic> or <italic>𝒜</italic>2 ⊆ <italic>𝒫</italic> or <italic>𝒜</italic>3 ⊆ <italic>𝒫</italic> for all ideals <italic>𝒜</italic>1<italic>, 𝒜</italic>2 and <italic>A</italic>3 of <italic>𝒭</italic>.
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In this paper we analyze strongly 2-absorbing prime ideals (shortly strongly 2-API), strongly 2-absorbing weak prime ideals (shortly strongly 2-AWPI) and 2-absorbing weak prime ideals (shortly 2-AWPI) in a non-commutative ring, which represent generalization of prime ideals (shortly PI) in a non-commutative ring. The relationship between the strongly 2-API and the 2-absorbing prime ideal (shortly 2-API) is examined. We provide examples to illustrate the new concept of strongly ma1-system and strongly ma2-system as well as the relationships beween them. Let I be an ideal of 𝒭 and 𝒨 be a strongly ma1-system such that I ∩ 𝒨 = ϕ. Then there exists a strongly 2-API 𝒫 of 𝒭 containing I such that 𝒫 ∩ 𝒨 = ϕ. We prove that 𝒫 is a strongly 2-API if and only if 𝒜1𝒜2𝒜3 ⊆ 𝒫 implies that 𝒜1 ⊆ 𝒫 or 𝒜2 ⊆ 𝒫 or 𝒜3 ⊆ 𝒫 for all ideals 𝒜1, 𝒜2 and A3 of 𝒭.

On Various 2-absorbing prime ideals in non commutative rings

Department of Applied Mathematics With Oceanology and Computer Programming

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 Various 2-absorbing prime ideals in non commutative rings"}

In this paper we analyze strongly 2-absorbing prime ideals (shortly strongly 2-API), strongly 2-absorbing weak prime ideals (shortly strongly 2-AWPI) and...

On Various 2-absorbing prime ideals in non commutative rings

Publié en ligne: 27 mars 2023

Pages: 141 - 154

Reçu: 23 juil. 2022

Accepté: 29 déc. 2022

DOI: https://doi.org/10.2478/auom-2023-0024

Mots clés
strongly 2-API, strongly 2-AWPI, 2-AWPI, strongly -system, strongly -system, weak -system, weak -system

© 2023 M. Palanikumar et al., published by Sciendo

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

On Various 2-absorbing prime ideals in non commutative rings

Publié en ligne: 27 mars 2023

Pages: 141 - 154

Reçu: 23 juil. 2022

Accepté: 29 déc. 2022

DOI: https://doi.org/10.2478/auom-2023-0024

Mots clésstrongly 2-API, strongly 2-AWPI, 2-AWPI, strongly -system, strongly -system, weak -system, weak -system

© 2023 M. Palanikumar et al., published by Sciendo

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

Mots clés
strongly 2-API, strongly 2-AWPI, 2-AWPI, strongly -system, strongly -system, weak -system, weak -system