| 局部有限 BL-代数的素逆演绎系统及性质 |
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| 引用本文： | 文贤红,吴洪博.局部有限 BL-代数的素逆演绎系统及性质[J].山东大学学报(自然科学版),2014(2):36-41. |
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| 作者姓名： | 文贤红 吴洪博 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,陕西西安710062 |
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| 基金项目： | 国家自然科学基金资助项目（11171196）;陕西省自然科学基础研究计划项目（2013JM1023） |
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| 摘 要： | 在BL-代数中引入逆演绎系统及素逆演绎系统的概念，并在局部有限BL-代数中研究了素逆演绎系统的基本性质及逆演绎系统和通常理想之间的关系；其次，讨论了BL-代数中逆演绎系统和同余关系之间相互决定的关系；最后，证明了由素逆演绎系统诱导的商代数为线性BL-代数，进而证明了在局部有限BL-代数中一个逆演绎系统是素逆演绎系统当且仅当由其诱导的商代数是线性的BL-代数。
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| 关 键 词： | BL-代数 局部有限 逆演绎系统 素逆演绎系统 同余关系 商代数 |
The prime reverse deductive system of locally finite BL-algebras with properties |
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| WEN Xian-hong,WU Hong-bo.The prime reverse deductive system of locally finite BL-algebras with properties[J].Journal of Shandong University(Natural Science Edition),2014(2):36-41. |
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| Authors: | WEN Xian-hong WU Hong-bo |
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| Institution: | (College of Mathematics and Information Science, Shaanxi Normal University, Xi＇an 710062, Shaanxi, China) |
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| Abstract: | Firstly, the concepts of reverse deductive system and prime reverse deductive system are introduced to BL-al-gebra.The basic properties of prime reverse deductive system and the relationship between reverse deductive and com-mon ideal in locally finite BL-algebras are investigated.Secondly, the connection between reverse deductive system and congruence relations is discussed.At last, it is proved that the quotient algebra determined by prime reverse deductive system is linear BL-algebra, and that in a locally finite BL-algebra a reverse deductive system is prime reverse deductive system if and only if the quotient algebra determined by itself is a linear BL-algebra. |
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| Keywords: | BL-algebra locally finite reverse deductive system prime reverse deductive system congruence relation quotient algebra |
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