Every complete atomic Boolean algebra is the ideal lattice of a cBCK-algebra
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866911939320348672 |
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| author | Evans, C. Matthew |
| author_facet | Evans, C. Matthew |
| contents | Given a complete atomic Boolean algebra, we show there is a commutative BCK-algebra whose ideal lattice is that Boolean algebra. This result is shown to exist within a larger framework involving BCK-algebras of functions, whose ideals and prime ideals are analyzed by way of a specific Galois connection. As a corollary of the main theorem, we show that every discrete topological space is the prime spectrum of a cBCK-algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_09291 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Every complete atomic Boolean algebra is the ideal lattice of a cBCK-algebra Evans, C. Matthew Rings and Algebras 06F35, 08A30, 06E99 Given a complete atomic Boolean algebra, we show there is a commutative BCK-algebra whose ideal lattice is that Boolean algebra. This result is shown to exist within a larger framework involving BCK-algebras of functions, whose ideals and prime ideals are analyzed by way of a specific Galois connection. As a corollary of the main theorem, we show that every discrete topological space is the prime spectrum of a cBCK-algebra. |
| title | Every complete atomic Boolean algebra is the ideal lattice of a cBCK-algebra |
| topic | Rings and Algebras 06F35, 08A30, 06E99 |
| url | https://arxiv.org/abs/2109.09291 |