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- Title
On Various 2-absorbing prime ideals in non commutative rings.
- Authors
Palanikumar, M.; Jana, Chiranjibe; Pal, Madhumangal; Leoreanu-Fotea, V.
- Abstract
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 R and M be a strongly ma1-system such that I ∩M = φ. Then there exists a strongly 2-API P of R containing I such that P ∩ M = 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 R.
- Subjects
PRIME ideals; COMMUTATIVE rings; NONCOMMUTATIVE rings
- Publication
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023, Vol 31, Issue 2, p141
- ISSN
1224-1784
- Publication type
Article
- DOI
10.2478/auom-2023-0024