Communications of the Korean Mathematical Society (대한수학회논문집)
- Volume 11 Issue 3
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- Pages.595-600
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- 1996
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
On deductive systems of hilbert algebras
- Hong, Sung-Min (Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University) ;
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Jun, Young-Bae
(Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University)
- Published : 1996.07.01
Abstract
We give a characterization of a deductive system. We introduce the concept of maximal deductive systems and show that every bounded Hilbert algebra with at least two elements contains at least one maximal deductive system. Moreover, we introduce the notion of radical and semisimple in a Hilbert algebra and prove that if H is a bounded Hilbert algebra in which every element is an involution, then H is semisimple.