对合m-半格中特殊元、理想及其范畴性质

doi:10.6040/j.issn.1671-9352.0.2022.590

摘要/Abstract

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$\ll、\unlhd$, 讨论对合m-半格中对合运算*与特殊元及$\ll、\unlhd$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。

关键词: 对合m-半格, 理想, 滤子, 范畴, 极限

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 $\ll$and $\unlhd$are defined in involutive m-semilattices, and the interrelationships between the involutive m-semilattices *, special element and$\ll、\unlhd$ 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 filters 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.

Key words: involutive m-semilattice, ideal, filter, category, limit

中图分类号:

O153.1

梁少辉,张雪亭,夏小刚. 对合m-半格中特殊元、理想及其范畴性质[J]. 《山东大学学报(理学版)》, 2024, 59(4): 1-8.

Shaohui LIANG,Xueting ZHANG,Xiaogang XIA. Special elements, ideals in involutive m-semilattices and its categorical properties[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(4): 1-8.

图/表 2

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图2

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