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Some results in local Hilbert algebras

In: Mathematica Slovaca, vol. 67, no. 3
Ali Soleimani Nasab - Arsham Borumand Saeid
Detaily:
Rok, strany: 2017, 541 - 552
Kľúčové slová:
Hilbert algebra (with supremum), local Hilbert algebra
O článku:
In this paper, we study local Hilbert algebras and give some theorems that characterize local Hilbert algebras. Also, we prove that, (i) $H$ is a local Hilbert algebra if and only if the set of all dense elements of $H$ is $H\smallsetminus \{0\}$. (ii) $H$ is a local Hilbert algebra if and only if the set of all regular elements of $H$ is a local Boolean algebra. In a local Hilbert algebra $H$ with supremum, we prove that: (i) If $F$ is a Boolean filter of $H$, then $F$ is a prime filter. (ii) $F$ is a Boolean filter iff $F$ is a maximal filter iff $F= H\smallsetminus \{0\}$.
Ako citovať:
ISO 690:
Nasab, A., Saeid, A. 2017. Some results in local Hilbert algebras. In Mathematica Slovaca, vol. 67, no.3, pp. 541-552. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0288

APA:
Nasab, A., Saeid, A. (2017). Some results in local Hilbert algebras. Mathematica Slovaca, 67(3), 541-552. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0288
O vydaní:
Publikované: 27. 6. 2017