Abstract
The functor on the category of bounded lattices induced by reversing their order, gives rise to a natural equivalence of coherent frames. We investigate the spectra as well as some well-known frame properties like zero-dimensionality and normality.
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Banaschewski B.: Ring theory and pointfree topology. Top. Appl. 137, 21–37 (2004)
Banaschewski B.: Gelfand and exchange rings: their spectra in pointfree topology. Arab. J. Sci. Eng. Sect. C Theme Issues 25(2), 3–22 (2000)
Banaschewski B.: Radical ideals and coherent frames. Comment. Math. Univ. Carolin. 37(2), 349–370 (1996)
Bhattacharjee, P.: Minimal prime element space of an algebraic frame (submitted)
Bhattacharjee, P.: Rigid extensions of algebraic frames. Algebra Universalis (in press)
Birkhoff, G.: Lattice Theory, 3rd edn. Colloquium Publications, vol. 25. (1967)
9th annual International Conference on ORD/OAL, The Frames and Spaces of Ordered Algebraic Structures - A Celebration of the 80th Birthday of Bernhard Banaschewski, Gainesville, FL (2006)
Grätzer, G.: General Lattice Theory. Academic Press Inc. (1978)
Iberkleid, W., McGovern, W. Wm.: Classes of Commutative Clean Rings (in press)
Iberkleid W., McGovern W. Wm.: A generalization of the Jaffard-Ohm-Kaplansky Theorem. Algebra Universalis 61, 201–212 (2009)
Johnstone P.J.: Stone Spaces. Cambridge Studies in Adv. Math., vol. 3. (1982)
Knox M. L., McGovern W. Wm.: Feebly projectable algebraic frames and multiplicative filters of ideals. Appl. Cat. Structures 15, 3–17 (2007)
Martinez J.: Archimedean lattices. Algebra Universalis 3, 247–260 (1973)
Martinez J., Zenk E.R.: When an Algebraic Frame is Regular. Algebra Universalis 50, 231–257 (2003)
McGovern W. Wm.: Neat rings. J. Pure Applied Alg. 205, 243–265 (2003)
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Presented by J. Martinez.
In memory of Paul F. Conrad
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Iberkleid, W., McGovern, W.W. A natural equivalence for the category of coherent frames. Algebra Univers. 62, 247–258 (2009). https://doi.org/10.1007/s00012-010-0058-3
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DOI: https://doi.org/10.1007/s00012-010-0058-3