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Normal Ideals of Pseudo-Complemented Distributive Lattices

CJM Vol. 9 (December 2017) [1], pp. 61 – 73.

Author(s): 
M. Sambasiva Rao [2]
Abd El-Mohsen Badawy [3]

Abstract: 

The notion of normlets and normal ideals are introduced in a pseudocomplemented distributive lattice and then normal ideals are characterized in terms of normlets. Some equivalent conditions are derived for a pseudo-complemented lattice to become a disjunctive lattice. The properties of direct products of normal ideals are studied. A set of equivalent conditions is derived for every prime normal ideal to become a minimal prime ideal in topological terms.

Keywords: 
pseudo-complemented distributive lattice [4]
normal ideal [5]
normlet [6]
direct product [7]
minimal prime ideal [8]
Hausdorff space [9]

2010 Mathematics Subject Classification: 
06B10 [10]
06D15 [11]
06D99 [12]

Full Paper (PDF): 
AttachmentSize
PDF icon CJM-Vol 9-2017_05.pdf [13]139.12 KB

Source URL: https://math.sc.chula.ac.th/cjm/content/normal-ideals-pseudo-complemented-distributive-lattices

Links
[1] http://www.math.sc.chula.ac.th/cjm/vol9
[2] https://math.sc.chula.ac.th/cjm/tags/m-sambasiva-rao
[3] https://math.sc.chula.ac.th/cjm/tags/abd-el-mohsen-badawy
[4] https://math.sc.chula.ac.th/cjm/tags/pseudo-complemented-distributive-lattice
[5] https://math.sc.chula.ac.th/cjm/tags/normal-ideal
[6] https://math.sc.chula.ac.th/cjm/tags/normlet
[7] https://math.sc.chula.ac.th/cjm/tags/direct-product
[8] https://math.sc.chula.ac.th/cjm/tags/minimal-prime-ideal
[9] https://math.sc.chula.ac.th/cjm/tags/hausdorff-space
[10] https://math.sc.chula.ac.th/cjm/tags/06b10
[11] https://math.sc.chula.ac.th/cjm/tags/06d15
[12] https://math.sc.chula.ac.th/cjm/tags/06d99
[13] https://d2ijd3g5wqapxj.cloudfront.net/cjm/sites/www.math.sc.chula.ac.th.cjm/files/CJM-Vol%209-2017_05.pdf