On semisubtractive ideals of semirings
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914956292653056 |
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| author | Goswami, Amartya |
| author_facet | Goswami, Amartya |
| contents | Our aim in this paper is to explore semisubtractive ideals of semirings. We prove that they form a complete modular lattice. We introduce Golan closures and prove some of their basic properties. We explore the relations between $Q$-ideals and semisubtractive ideals of semirings, and also study them in $s$-local semirings. We introduce two subclasses of semisubtractive ideals: $s$-strongly irreducible and $s$-irreducible, and provide various representation theorems. By endowing a topology on the set of semisubtractive ideals, we prove that the space is $T_0$, sober, connected, and quasi-compact. We also briefly study continuous maps between semisubtractive spaces. We construct $s$-congruences and prove a bijection between these congruences and semisubtractive ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16192 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On semisubtractive ideals of semirings Goswami, Amartya Commutative Algebra Rings and Algebras 16Y60 Our aim in this paper is to explore semisubtractive ideals of semirings. We prove that they form a complete modular lattice. We introduce Golan closures and prove some of their basic properties. We explore the relations between $Q$-ideals and semisubtractive ideals of semirings, and also study them in $s$-local semirings. We introduce two subclasses of semisubtractive ideals: $s$-strongly irreducible and $s$-irreducible, and provide various representation theorems. By endowing a topology on the set of semisubtractive ideals, we prove that the space is $T_0$, sober, connected, and quasi-compact. We also briefly study continuous maps between semisubtractive spaces. We construct $s$-congruences and prove a bijection between these congruences and semisubtractive ideals. |
| title | On semisubtractive ideals of semirings |
| topic | Commutative Algebra Rings and Algebras 16Y60 |
| url | https://arxiv.org/abs/2409.16192 |