1
Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.
2
Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran.
Abstract
In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L), which is ring of real-valued continuous functions for frame L, does not have more than one element. Also, z-filters are introduced in terms of pointfree topology. Then the relationship between z-filters and ideals, particularly maximal ideals, is examined. Finally, it is shown that the family of all zero sets is a base for the collection of closed sets.
Estaji, A. A., Karimi Feizabadi, A., & Abedi, M. (2015). Zero sets in pointfree topology and strongly $z$-ideals. Bulletin of the Iranian Mathematical Society, 41(5), 1071-1084.
MLA
Estaji, A. A., Karimi Feizabadi, A., & Abedi, M. "Zero sets in pointfree topology and strongly $z$-ideals", Bulletin of the Iranian Mathematical Society, 41, 5, 2015, 1071-1084.
HARVARD
Estaji A. A., Karimi Feizabadi A., Abedi M. (2015). 'Zero sets in pointfree topology and strongly $z$-ideals', Bulletin of the Iranian Mathematical Society, 41(5), pp. 1071-1084.
CHICAGO
A. A. Estaji, A. Karimi Feizabadi & M. Abedi, "Zero sets in pointfree topology and strongly $z$-ideals," Bulletin of the Iranian Mathematical Society, 41 5 (2015): 1071-1084,
VANCOUVER
Estaji A. A., Karimi Feizabadi A., Abedi M. Zero sets in pointfree topology and strongly $z$-ideals. BIMS. 2015;41(5):1071-1084.
