Zariski-Like Topology on S-Quasi-Primary Ideals of a Commutative Ring
Let R be a commutative ring with nonzero identity and, S⊆R be a multiplicatively closed subset. An ideal P of R is called an S-quasi-primary ideal if P∩S=∅ and there exists an (fixed) s∈S and whenever ab∈P for a,b∈R then either sa∈P or sb∈P. In this paper, we construct a topology on the set QPrimSR...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9177320 |
| Summary: | Let R be a commutative ring with nonzero identity and, S⊆R be a multiplicatively closed subset. An ideal P of R is called an S-quasi-primary ideal if P∩S=∅ and there exists an (fixed) s∈S and whenever ab∈P for a,b∈R then either sa∈P or sb∈P. In this paper, we construct a topology on the set QPrimSR of all S-quasi-primary ideals of R which is a generalization of the S-prime spectrum of R. Also, we investigate the relations between algebraic properties of R and topological properties of QPrimSR like compactness, connectedness and irreducibility. |
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| ISSN: | 2314-4785 |