半群的L-模糊理想
L-Fuzzy Ideals of Semigroups
DOI: 10.12677/PM.2021.116124, PDF, HTML,   
作者: 李倩倩：兰州理工大学理学院，甘肃 兰州
关键词: 半群；L-模糊子集；L-模糊理想；Semigroup； L-Fuzzy Subset； L-Fuzzy Ideal
摘要: 设S是半群, L是完全格, 这篇文章研究了半群S的L-模糊理想, 在此基础上, 我们研究了L-模糊理想在普通半群以及几类特殊半群上的性质. 定义了两个L-模糊子集的“◦”运算. 给出了L-模糊理想和几类特殊的L-模糊理想的概念以及他们的等价定义. 证明了半群S的每个L-模糊双边理想都是L-模糊内禀理想, 每个L-模糊左（右）理想都是L-模糊拟理想, 每个L-模糊双理想都是L-模糊广义双理想, 每个L-模糊拟理想都是L-模糊双理想.
Abstract: Let S be a semigroup and L be a complete lattice. In this paper, we study L-fuzzy ideals on a semigroup. On this basis, we study properties of L-fuzzy ideals on ordinary semigroups and several types special semigroups are discussed. This article defines the “◦” of two L-fuzzy subsets. The concepts of L-fuzzy ideals and several special L-fuzzy ideals and their equivalent definitions are given. It is proved that every L-fuzzy ideal of the semigroup S is a L-fuzzy interior ideal, and every L-fuzzy left (right) ideal is a L-fuzzy quasi-ideal. Every L-fuzzy bi-ideal is a L-fuzzy generalized bi-ideal, and every L-fuzzy quasi-ideal is a L-fuzzy bi-ideal.
文章引用：李倩倩. 半群的L-模糊理想[J]. 理论数学, 2021, 11(6): 1103-1111. https://doi.org/10.12677/PM.2021.116124

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