Direct limits of generalized pseudo-effect algebras with the Riesz decomposition properties
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In this paper, we focus on direct limits and inverse limits in the category with generalized pseudo-effect algebras (GPEAs for short) as objects and GPEA-morphisms as morphisms. We show that direct limits exist in the category of GPEAs and direct limits of GPEAs satisfy the Riesz decomposition properties whenever the directed systems of GPEAs satisfy the Riesz decomposition properties. Then, we give a condition under which the quotient of a direct limit of GPEAs is a direct limit of quotients of GPEAs. Moreover, we prove that if inverse systems of GPEAs satisfy the Riesz decomposition properties, then inverse limits also satisfy the Riesz decomposition properties.
KeywordsGeneralized pseudo-effect algebras Riesz decomposition properties Direct limits Inverse limits
This article does not contain any studies with human participants or animals performed by any of the authors. Informed consent was obtained from all individual participants included in the study. The authors are grateful to the anonymous referee’s valuable and constructive comments. This work is partially by National Science Foundation of China (Grant Nos. 61673250, 11201279) and the Fundamental Research Funds for the Central Universities (Grant No. GK201503017)
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Conflict of interest
The authors declare that they have no conflict of interest.
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