JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (2): 1-8.doi: 10.6040/j.issn.1671-9352.0.2023.342

   

On the properties of S-hyperlattice ideals

LIU Ni, CUI Panpan   

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Published:2025-02-14

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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

CLC Number: 

  • O153.1
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