| 摘要: |
| 本文研究了R0代数上有关态算子的问题.利用MV-代数上内态的引入方法引入了态算子，定义了态R0代数，它是R0代数的一般化.给出了一些非平凡态R0代数的例子并讨论了态R0代数的一些基本性质.在此基础上给出了态滤子和态局部R0代数的概念，并利用态滤子刻画了态局部R0代数.推广了局部R0代数的相关理论. |
| 关键词: R0代数 态R0代数 态滤子 态局部 |
| DOI： |
| 分类号:O141.1 |
| 基金项目:国家自然科学基金资助（11571281）. |
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| ON STATE R0-ALGEBRAS |
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QIN Yu-jing1, XIN Xiao-long1, HE Peng-fei2
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1.School of Mathematics, Northwest University, Xi'an 710127, China;2.School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, China
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| Abstract: |
| In this paper, we study the problems of state operators. By using the method of introducing internal states on MV-algebras, we introduce the state operators on R0-algebras and deflne the state R0-algebras, which are generalization of R0-algebras. We give some non-trivial examples of state R0-algebras and study some basic properties of them. Based on the above arguments we deflne the state fllters and state local R0-algebras. We characterise the state local R0-algebras by the state fllters, which generalizes the theory of local R0-algebras. |
| Key words: R0-algebra state R0-algebra state fllter state local |
