Abstract
The aim of this paper is to introduce the notion of states on R 0 algebras and investigate some of their properties. We prove that every R 0 algebra possesses at least one state. Moreover, we investigate states on weak R 0 algebras and give some examples to show that, in contrast to R 0 algebras, there exist weak R 0 algebras which have no states. We also derive the condition under which finite linearly ordered weak R 0 algebras have a state.
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This work is supported by NSFC (No.60605017).
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Lianzhen, L., Xiangyang, Z. States on R 0 algebras. Soft Comput 12, 1099–1104 (2008). https://doi.org/10.1007/s00500-008-0276-1
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DOI: https://doi.org/10.1007/s00500-008-0276-1