基于L-值泛代数的L-值模  

L⁃valued modules based on L⁃valued universal algebras

作　　者：周鑫 刘淼 ZHOU Xin;LIU Miao(College of Mathematics and Statistics,Yili Normal University,Yining 835000,Xinjiang,China;Institute of Applied Mathe-matics,Yili Normal University,Yining 835000,Xinjiang,China)

机构地区：[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

出　　处：《山东大学学报（理学版）》2023年第3期48-54,共7页Journal of Shandong University(Natural Science)

基　　金：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)。

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。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.

关 键 词：模糊集 L-值集 L-值泛代数 L-值模 模糊恒等式 

分 类 号：O159[理学—数学]