Simple and sub-directly irreducible double Boolean algebras
| Autor: | Kembang, G. T., Kwuida, L., Temgoua, E. R. A., Tenkeu, Y. L. J. |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | Double Boolean algebras are algebras $\underline{D}=(D;\sqcap,\sqcup,\neg,\lrcorner,\bot,\top)$ of type $(2,2,1,1,0,0)$ introduced by Rudolf Wille to capture the equational theory of the algebra of protoconcepts. Every double Boolean algebra $\underline{D}$ contains two Boolean algebras denoted by $\underline{D}_{\sqcap}$ and $\underline{D}_{\sqcup}$. A double Boolean algebra $\underline{D}$ is said pure if $D=D_{\sqcap}\cup D_{\sqcup}$, and trivial if $\bot\sqcup\bot=\top\sqcap\top$. In this work, we first show that a double Boolean algebra is pure and trivial if and only if it is a glued sum of two Boolean algebras; secondly, we characterize simple double Boolean algebras; and finally, we determine up to isomorphism all sub-directly irreducible algebras of some sub-classes of the variety of double Boolean algebras. Comment: 18 pages, 3 figures, 19 tables |
| Databáze: | arXiv |
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