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中文摘要：
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。
英文摘要：
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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