A new class of BL-algebras

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• 作者：Somayeh Motamed ; Lida Torkzadeh
• 关键词：RS ; BL ; algebra ; Semi RS ; BL ; algebra ; Right (left) stabilizer ; Semi stabilizer filter ; Stabilizer filter
• 刊名：Soft Computing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：21
• 期：3
• 页码：687-698
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Computational Intelligence; Artificial Intelligence (incl. Robotics); Mathematical Logic and Foundations; Control, Robotics, Mechatronics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1433-7479
• 卷排序：21

文摘

In this paper, we introduce the notion of right stabilizers in BL-algebras and define a class of BL-algebras, called RS-BL-algebra. Then we investigate the relationships between the right and left stabilizers in BL-algebras. After that we define the concept of semi RS-BL-algebras and we prove that semisimple BL-algebras and semi RS-BL-algebras are RS-BL-algebra. Moreover, every finite RS-BL-algebra is a semi RS-BL-algebra. Finally, we introduce the concept of a semi-stabilizer and a stabilizer filter in a BL-algebra and we state and prove some theorems which determine the relationships between this notion and the other types of filters of a BL-algebra.