Hilbert algebras with supremum generated by finite chains
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Hernando Gaitán
Abstract
Based on the work of A. Monteiro, A. Torrens, and D. Buşneag, in this paper we point out that the dual space of Hilbert algebras with supremum generated by chains depends, modulo the dual space of a Hilbert algebra with supremum defined by S. Celani an D. Montangie, exclusively, on the order carried out by the topological space. We use such a characterization to prove that a bounded Hilbert algebra generated by chains is determined by the monoid of its endomorphisms.
(Communicated by Jan Kühr )
Acknowledgements
The author wishes to express his gratitude to the referee for guiding him to find important references unknown to him which helped to simplify enormously the presentation of the preliminaries.
References
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Articles in the same Issue
- Regular papers
- On the finite embeddability property for quantum B-algebras
- A dual Ramsey theorem for finite ordered oriented graphs
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- The left Riemann-Liouville fractional Hermite-Hadamard type inequalities for convex functions
- A geometrical version of Hardy-Rellich type inequalities
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- Uniqueness of meromorphic functions sharing four small functions on annuli
- A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator
- Functions of bounded variation related to domains bounded by conic sections
- Unified solution of Fekete-Szegö problem for subclasses of starlike mappings in several complex variables
- Oscillatory criteria for the second order linear ordinary differential equations
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