Pointfree Spectra of Riesz Spaces

One of the best ways of studying ordered algebraic structures is through their spectra. The three well-known spectra usually considered are the Brumfiel, Keimel, and the maximal spectra. The pointfree versions of these spectra were studied by B. Banaschewski for f -rings. Here, we give the pointfree versions of the Keimel and the maximal spectra for Riesz spaces. Moreover, we briefly mention how one can use the results of this paper to give a pointfree version of the Kakutani duality for Riesz spaces. Mathematics Subject Classifications (2000): 06D22, 46A40, 46B40, 46B42. Key words: frame, Riesz space, uniform and bounded Riesz spaces, Keimel and maximal spectra.

• Type: Journal
• Year: 2004
• Where: ACS
• Authors: M. Mehdi Ebrahimi, A. Karimi, Mojgan Mahmoudi
• Keywords: ACS 2004, ACS 2007, Maximal Spectra, Pointfree Version, Riesz Spaces