中文摘要：

首先,本文讨论了弱MTL-代数的性质,并给出弱MTL-代数的等价刻画;其次,将蕴涵演绎系统的概念引入到弱MTL-代数中,并研究了演绎系统与蕴涵演绎系统的关系,且给出蕴涵演绎系统的几个等价条件;最后,讨论了弱MTL-代数中的演绎系统和同余关系之间的相互决定的关系,并证明了在弱MTL-代数中一个蕴涵演绎系统是素的当且仅当由其诱导的商代数是全序的弱MTL-代数。

英文摘要：

Firstly, in the present paper, some properties of weak MTL algebras are discussed, and several characterizations of weak MTL algebras are revealed. Secondly, the concept of implicative deductive systems is introduced into weak MTL algebras, and the relationships between deductive systems and implicative deductive systems are investigated, and some equivalent conditions of implicative deductive systems are given. Finally, the connection between deductive systems and congruence relations is discussed, it is proved that in a weak MTL algebra a implicative deductive system is prime if and only if the quotient algebra determined by itself is a liner weak MTL algebra.