| 基于L-值泛代数的L-值模 |
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| 引用本文： | 周鑫,刘淼.基于L-值泛代数的L-值模[J].山东大学学报(理学版),2023,58(3):48-54. |
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| 作者姓名： | 周鑫 刘淼 |
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| 作者单位： | 1. 伊犁师范大学数学与统计学院, 新疆 伊宁 835000;2. 伊犁师范大学应用数学研究所, 新疆 伊宁 835000 |
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| 基金项目： | 新疆维吾尔自治区自然科学基金资助项目(2020D01C269);新疆维吾尔自治区高校科研计划项目(XJEDU2021Y042);新疆伊犁州科技计划项目(YZ2022Y010);伊犁师范大学博士科研启动基金项目(2021YSBS011);伊犁师范大学科研创新团队项目(CXZK2021014);伊犁师范大学学实高层次人才岗位项目(YSXSGG22002) |
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| 摘 要： | L-值模是一类格值代数结构,定义在类似于模的泛代数上。首先,将经典数学中等式用模糊恒等式替代,基于L-值泛代数给出了L-值模的概念。其次, 通过模糊代数的商结构给出了L-值泛代数是L-值模的充分必要条件。 再者,给出了L-值模的基本性质。 最后, 给出了L-值子模的刻画。
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| 关 键 词： | 模糊集 L-值集 L-值泛代数 L-值模 模糊恒等式 |
L-valued modules based on L-valued universal algebras |
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| ZHOU Xin,LIU Miao.L-valued modules based on L-valued universal algebras[J].Journal of Shandong University,2023,58(3):48-54. |
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| Authors: | ZHOU Xin LIU Miao |
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| Institution: | 1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China;2. Institute of Applied Mathematics, Yili Normal University, Yining 835000, Xinjiang, China |
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| Abstract: | L-valued modules are lattice-valued algebraic structures, defined on universal algebras of the same type as modules, but which are not necessary modules. First, the classical equality is replaced by a fuzzy identity, and the concept of L-valued modules are given based on L-valued universal algebras. Next, the necessary and sufficient conditions for L-valued universal algebras to be L-valued modules are given by using quotient structure of fuzzy algebras. Furthermore, this gives some basic properties of L-valued modules. Finally, we shows the structure of L-valued submodules. |
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| Keywords: | fuzzy set L-valued set L-valued universal algebra L-valued module fuzzy identity |
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