Some results in local Hilbert algebras

Rok, strany: 2017, 541 - 552

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 $F= H\smallsetminus \{0\}$.

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