Joins and meets in effect algebras
Autor: | Binczak, Grzegorz, Kaleta, Joanna, Zembrzuski, Andrzej |
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Rok vydání: | 2021 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | We know that each effect algebra $E$ is isomorphic to $\pi(X)$ for some $E$-test spaces $(X,{\cal T})$.We describe when $\pi(x)\lor \pi(y)$ and $\pi(x)\land\pi(y)$ exists for $x,y\in{\cal E}(X,{\cal T})$. Moreover we give the formula for $\pi(x)\lor\pi(x)$ and $\pi(x)\land\pi(y)$ using only $x,y$ and tests which are elements of ${\cal T}$. We obtain an example of finite, not homogeneous effect algebra $E$ such that sharp elements of $E$ form a lattice, whereas $E$ is not a lattice. |
Databáze: | arXiv |
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