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中文摘要：
首先给出反软子格的新概念以及两个反软子格分别在限制并和或的运算下仍然是反软子格。其次利用软集的反对偶给出反软子格的等价刻画。再次利用软集的反扩张原理给出反软子格在同态映射下像与原像的性质。最后在全体反软子格组成的集合H上引入链条件并讨论H是阿丁的或诺特的充要条件。
英文摘要：
Firstly,the definition of anti-soft sublattices is given,and we give that the restricted union and OR of two anti-soft sublattices are still anti-soft sublattices.Then we give the equivalent characterizations of anti-soft sublattices based on the anti-dual of soft set.In addition,based on the anti-extension principle,the properties of their image and inverse image are given under the homomorphic mapping.Finally,we introduce the condition of chain over H which is consisted of all of the anti-soft sublattices and discuss the necessary sufficient condition that His Artin or Noether.
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