Volume 5, Issue 1 (Vol. 5, No. 1 2019)                   mmr 2019, 5(1): 53-66 | Back to browse issues page


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Abedi M, Estaji A A. Ompactification of Completely Regular Frames based on their Cozero Part. mmr 2019; 5 (1) :53-66
URL: http://mmr.khu.ac.ir/article-1-2607-en.html
1- Esfarayen University of Technology , abedi@esfarayen.ac.ir
2- Hakim Sabzevari University
Abstract:   (2010 Views)

 Let L  be a frame. We denoted the set of all regular ideals of cozL by rId(cozL) . The aim of this paper is to study these ideals. For a  frame L , we show that  rId(cozL) is a compact completely regular frame and the map jc : rId(cozL)→L  given by jc (I)=⋁I   is a compactification of L which is isomorphism to its  Stone–Čech compactification and is proved that jc have a right adjoint rc : L → rId(cozL) , given by rc(a)={x∈cozL : x≺≺a}. Moreover we identify prime and compact elements of rId(cozL) and we investigate the relation between regular ideals of cozL and P-frames. In addition it is shown that  a  frame L  is a P-frame if and only if any ideal of cozL is regular../files/site1/files/51/%D8%B9%D8%A7%D8%A8%D8%AF%DB%8C.pdf

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Type of Study: Original Manuscript | Subject: alg
Received: 2017/03/27 | Revised: 2019/07/9 | Accepted: 2018/06/27 | Published: 2019/07/13 | ePublished: 2019/07/13

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