| 格蕴涵代数中的极小素理想及α-理想 |
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| 引用本文： | 孟彪龙,付巧峰,梁少辉.格蕴涵代数中的极小素理想及α-理想[J].计算机工程与应用,2018,54(16):44-48. |
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| 作者姓名： | 孟彪龙 付巧峰 梁少辉 |
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| 作者单位： | 西安科技大学 数学系，西安 710054 |
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| 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。
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| 关 键 词： | 极小素理想 零化子 [&alpha ]-理想 拓扑空间 |
Minimal prime ideals and [α]-ideals in lattice implication algebras |
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| MENG Biaolong,FU Qiaofeng,LIANG Shaohui.Minimal prime ideals and [α]-ideals in lattice implication algebras[J].Computer Engineering and Applications,2018,54(16):44-48. |
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| Authors: | MENG Biaolong FU Qiaofeng LIANG Shaohui |
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| Affiliation: | Department of Mathematics, Xi’an University of Science and Technology, Xi’an 710054, China |
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| 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 beingα]-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. |
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| Keywords: | minimal prime ideal annihilator [α]-ideal topology space |
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