S-超格理想的相关性质

doi:10.6040/j.issn.1671-9352.0.2023.342

摘要/Abstract

摘要： 本文对S-超格理想的性质进行了探究。证明了两个S-超格的S-超格理想的直积是它们直积的S-超格理想,S-超格理想在S-超格满同态下的像和原像仍为S-超格理想,任意S-超格的全体S-超格理想构成一个代数的有顶交结构。举例说明了对于S-超格同余,最小元0所在的同余类一般不是S-超格理想,并给出了它是S-超格理想的一个充分条件,同时对任意S-超格理想,构造了以其为同余类的最大的S-超格同余。

关键词: 超格, S-超格, S-超格理想, S-超格同余, 交结构

Abstract: In this paper, the properties of S-hyperlattice ideals are explored. It is proved that the direct product of S-hyperlattice ideals of two S-hyperlattices is an S-hyperlattice ideal of their direct product, the homomorphic image and preimage of S-hyperlattice ideal are still S-hyperlattice ideals, the set of all S-hyperlattice ideals of an S-hyperlattice is an algebraic topped meet structure. It is illustrated that for an S-hyperlattice congruence, the congruence class of the smallest element zero is generally not an S-hyperlattice ideal, and a sufficient condition for it to be an S-hyperlattice ideal is given. While for an S-hyperlattice ideal, a maximal S-hyperlattice congruence with it as a congruence class is constructed.

Key words: hyperlattice, S-hyperlattice, S-hyperlattice ideal, S-hyperlattice congruence, meet structure

中图分类号:

O153.1

刘妮,崔盼盼. S-超格理想的相关性质[J]. 《山东大学学报(理学版)》, 2025, 60(2): 1-8.

LIU Ni, CUI Panpan. On the properties of S-hyperlattice ideals[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(2): 1-8.

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