对合m-半格中特殊元、理想及其范畴性质
Special elements,ideals in involutive m-semilattices and its categorical properties
梁少辉 1张雪亭 1夏小刚1
作者信息
- 1. 西安科技大学理学院,陕西西安 710100
- 折叠
摘要
给出对合m-半格的概念,得到对合m-半格的一系列重要性质.定义合m-半格中2种序关系(《)、(≤),讨论对合m-半格中对合运算*与特殊元及(《)、(≤)的相互关系.利用特殊元构造子对合m-半格,研究对合m-半格中理想和滤子的结构,得到利用元素生成理想和滤子的具体形式,引入对合m-半格范畴的定义,探讨对合m-半格范畴中乘积的具体形式,得到对合m-半格范畴的极限结构,证明对合m-半格范畴是完备的.
Abstract
The concept of involutive m-semilattices is given,and a series of important properties of involutive m-semilattices are obtained.The two order relationships(《)and(≤)are defined in involutive m-semilattices,and the interrelationships between the invo-lutive m-semilattices*,special element and(《)、(≤)are discussed.The subinvolutive m-semilattices are constructed by using special elements.The structures of ideals and filters in involutive m-semilattices are studied,the concrete forms of generating ideals and fil-ters from elements are obtained.The definition of the category of involutive m-semilattices is introduced,and the specific form of the product of the category of involutive m-semilattices is discussed,and the limit structure of the category of involutive m-semilattices is obtained.It is proved that the category of involutive m-semilattices is complete.
关键词
对合m-半格/理想/滤子/范畴/极限Key words
involutive m-semilattice/ideal/filter/category/limit引用本文复制引用
基金项目
国家自然科学基金(52074211)
陕西省教育厅科研项目(17JK0510)
出版年
2024
NETL
NSTL
万方数据