Computer Engineering and Applications ›› 2018, Vol. 54 ›› Issue (16): 44-48.DOI: 10.3778/j.issn.1002-8331.1706-0240

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Minimal prime ideals and [α]-ideals in lattice implication algebras

MENG Biaolong, FU Qiaofeng, LIANG Shaohui   

  1. Department of Mathematics, Xi’an University of Science and Technology, Xi’an 710054, China
  • Online:2018-08-15 Published:2018-08-09



  1. 西安科技大学 数学系,西安 710054

Abstract: The equivalence of minimal prime ideals and minimal lattice prime ideals in lattice implication algebras is proved, then the reciprocal representation theorem of minimal prime ideals and annihilators is provided. The concept of [α]-ideal is proposed and several equivalent characterizations are established, also prime ideals being[α]-ideals are proved. The set [Sα(L)] of all prime [α]-ideals being a compact Stone space is proved, moreover the sufficient and necessary conditions for [Sα(L)] being [T1,T2] spaces respectively are obtained.

Key words: minimal prime ideal, annihilator, [α]-ideal, topology space

摘要: 在格蕴涵代数中,证明了极小素理想与极小格素理想的等价性,继而给出了极小素理想与零化子的相互表示定理。提出了格蕴涵代数中的[α]-理想概念并给出其若干等价刻画,证明了极小素理想是[α]-理想。证明了全体素[α]-理想之集[Sα(L)]是一个紧的Stone空间,进一步给出[Sα(L)]分别是[T1、][T2]拓扑空间的充要条件。

关键词: 极小素理想, 零化子, [&alpha, ]-理想, 拓扑空间