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中文摘要：
研究了Quantale中的弱S-素元与极小弱S-素元的一些性质.给出了一类Quantale中的弱S-素元的等价刻画,证明了弱S-素元在满足一定条件的映射下的像仍然是弱S-素元以及当S具有左吸收性时,双侧元是弱S-素元当且仅当它是素元.得到了在幂等双侧Quantale中极大元是弱S-素元.同时,定义了本质弱S-素元,探讨了弱S-素元与本质弱S-素元之间的关系.
英文摘要：
Some properties of the weakly S-prime elements and the minimal weakly S-prime elements are studied.An equivalent description of the weakly S-prime elements is given.It is proved that a weakly S-prime element is preserved by the map between the quantales satisfying certain conditions and a two-sided element is weakly S-prime if and only if it is prime when S has the left absorbency.It is obtained that a maximal element is weakly S-prime in an idempotent two-sided quantale.At the same time,the concept of esse...
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