BN - 代数的（模糊）理想
(Fuzzy) Ideals of BN-Algebras.
作者信息
Dymek Grzegorz, Walendziak Andrzej
机构信息
Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Konstantynów 1H, 20-708 Lublin, Poland.
Institute of Mathematics and Physics, Siedlce University, 3 Maja 54, 08-110 Siedlce, Poland.
出版信息
ScientificWorldJournal. 2015;2015:925040. doi: 10.1155/2015/925040. Epub 2015 Jun 1.
The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained.
引入了BN - 代数中理想和模糊理想的概念。研究了它们的性质和特征。还研究了BN - 代数的正规理想和正规同余的概念，展示了它们的性质，并给出了它们之间的一一对应关系。给出了模糊集成为模糊理想的条件。建立了BN - 代数的理想与模糊理想之间的关系。给出了BN - 代数模糊理想的同态性质。最后，通过模糊理想得到了诺特BN - 代数和阿廷BN - 代数的特征。
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