Open Access
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A note on -filters and -ideals
*Ahmed MaatallahCorresponding authorahmedmaatallahsd93@gmail.comDepartment of MathematicsFaculty of Sciences5000 MonastirUniversity of MonastirTunisiaView full profile → , Ali Benhissiali benhissi@yahoo.frDepartment of MathematicsFaculty of Sciences5000 MonastirUniversity of MonastirTunisiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Nov 2020
- Accepted:
- 05 Mar 2021
- Published Online:
- 15 Nov 2021
- Article type:
- A
- Language:
- EN
- Article no.:
- JDMSC-1356
- Pages:
- 411–422
Abstract
Let R be a commutative ring with identity and Y ⊆ Spec(R). In this paper, we pay attention to the concept of -filters. First, as a generalization of a prime -filter, we define the concept of 2-absorbing -filters. We give a correspondence between the 2-absorbing -filters and the 2-absorbing strong -ideals. Furthermore, we give a condition under which every -filter containing a 2-absorbing -filter is also a 2-absorbing -filter. The second part of this paper deals with the case of the product rings. We define the product of and , denoted by . We prove that all the -filters on , where is a subset of the prime spectrum of the product rings, are all of the previous forms. As a natural result, we characterize all the prime -filters, -ultrafilters and 2-absorbing -filters.
Keywords
Subject Classifications
(2010) 13A1554C40
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