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| Abstract: |
| This study mainly focuses on the triangle bounded L-algebras and triangle ideals. Firstly, the definition of triangle bounded L-algebras is presented, and several examples with different conditions are outlined along with an exploration of their properties. Moreover, we investigate the structure of triangle bounded L-algebra with a special condition. Secondly, we define the concept of triangle ideals of triangle bounded L-algebra and explore the connection between the triangle ideals of triangle bounded L-algebra L and the ideals of bounded L-algebra E(L). In addition, we classified and studied various classes of triangle ideals, including Stonean triangle ideals, extended Stonean triangle ideals, and lattice ideals, and by introducing the notion of Stonean triangle bounded L algebras, we examine the relationship between Stonean triangle bounded L-algebras and Stonean triangle ideals. Finally, we investigate the interrelationships among these various types of triangle ideals. |
| Key words: triangle bounded L-algebra Stonean triangle bounded L-algebra triangle ideal (extended) Stonean triangle ideal lattice ideal |
| DOI：10.11916/j.issn.1005-9113.2024059 |
| Clc Number:O29 |
| Fund: |
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| Descriptions in Chinese: |
| 三角有界-代数与三角理想
陈昊 1，辛小龙1,2
(1.西安工程大学 ，理学院，西安，710048; 2.西安外事学院，商学院，西安，710127) 摘要：本文主要研究了三角有界L-代数与三角理想。首先，本文给出了三角有界L-代数的定义，并给出一些满足不同条件的三角有界L-代数的例子，探索它们的性质，并研究了满足特殊条件的三角有界L-代数的结构。其次，引入并研究了三角有界L-代数上的三角理想，并探讨了其与有界L-代数E(L)上的理想之间的关系。此外，对特殊的三角理想，包括Stonean三角理想，拓展Stonean三角理想以及格理想进行研究，进而引入Stonean三角有界L-代数的概念并研究了其与Stonean三角理想的关系。最后，本文探究了不同类型的三角理想之间的联系。 关键词：三角有界L-代数；Stonean三角有界L-代数；三角理想；(拓展) Stonean三角理想；格理想 |
