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Title

\mathcal{R}L- valued f-ring homomorphisms and lattice-valued maps

Year: 1396
COI: JR_CGASAT-7-1_007
Language: EnglishView: 15
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Authors

Abolghasem Karimi Feizabadi - Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran.
Ali Akbar Estaji - Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.
Batool Emamverdi - Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.

Abstract:

In this paper, for each {\it lattice-valued map} A\rightarrow L with some properties, a ring representation A\rightarrow \mathcal{R}L is constructed. This representation is denoted by \tau_c which is an f-ring homomorphism and a \mathbb Q-linear map, where its index c, mentions to a lattice-valued map. We use the notation \delta_{pq}^{a}=(a -p)^{+}\wedge (q-a)^{+}, where p, q\in \mathbb Q and a\in A, that is nominated as {\it interval projection}. To get a well-defined f-ring homomorphism \tau_c, we need such concepts as {\it bounded}, {\it continuous}, and \mathbb Q-{\it compatible} for c, which are defined and some related results are investigated. On the contrary, we present a cozero lattice-valued map c_{\phi}:A\rightarrow L for each f-ring homomorphism \phi: A\rightarrow \mathcal{R}L. It is proved that c_{\tau_c}=c^r and \tau_{c_{\phi}}=\phi, which they make a kind of correspondence relation between ring representations A\rightarrow \mathcal{R}L and the lattice-valued maps A\rightarrow L, Where the mapping c^r:A\rightarrow L is called a {\it realization} of c. It is shown that \tau_{c^r}=\tau_c and c^{rr}=c^r.   Finally, we describe how \tau_c can be a fundamental tool to extend pointfree version of Gelfand duality constructed by B. Banaschewski.  

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Paper COI Code

This Paper COI Code is JR_CGASAT-7-1_007. Also You can use the following address to link to this article. This link is permanent and is used as an article registration confirmation in the Civilica reference:

https://civilica.com/doc/1268007/

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Karimi Feizabadi, Abolghasem and Estaji, Ali Akbar and Emamverdi, Batool,1396,\mathcal{R}L- valued f-ring homomorphisms and lattice-valued maps,https://civilica.com/doc/1268007

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  • Banaschewski, B., Pointfree topology and the spectra of f-rings, Ordered ...
  • Banaschewski, B., The real numbers in pointfree topology, Texts in ...
  • Bigard, A., K. Keimel, and S. Wolfenstein, Groups et anneaux ...
  • Ebrahimi, M.M. and A. Karimi Feizabadi, Pointfree prime representation of ...
  • Gillman, L. and M. Jerison, "Rings of Continuous Function", Graduate ...
  • Karimi Feizabadi, A., Representation of slim algebraic regular cozero maps, ...
  • Karimi Feizabadi, A., Free lattice-valued functions, reticulation of rings and ...
  • Picado, J. and A. Pultr, "Frames and Locales: Topology without ...
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    Type of center: Azad University
    Paper count: 2,900
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