The lattice of ideals of certain rings
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917762057633792 |
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| author | Savin, Diana |
| author_facet | Savin, Diana |
| contents | Let $A$ be a unitary ring and let $(\mathbf{I(A),\subseteq })$ be the lattice of ideals of the ring $A.$ In this article we will study the property of the lattice $(\mathbf{I(A),\subseteq})$ to be Noetherian or not, for various types of rings $A$. In the last section of the article we study certain rings that are not Boolean rings, but all their ideals are idempotent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15145 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The lattice of ideals of certain rings Savin, Diana Commutative Algebra Logic Number Theory 11R04, 11R11, 03G05, 03B80, 11T30, 03G10 Let $A$ be a unitary ring and let $(\mathbf{I(A),\subseteq })$ be the lattice of ideals of the ring $A.$ In this article we will study the property of the lattice $(\mathbf{I(A),\subseteq})$ to be Noetherian or not, for various types of rings $A$. In the last section of the article we study certain rings that are not Boolean rings, but all their ideals are idempotent. |
| title | The lattice of ideals of certain rings |
| topic | Commutative Algebra Logic Number Theory 11R04, 11R11, 03G05, 03B80, 11T30, 03G10 |
| url | https://arxiv.org/abs/2303.15145 |