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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 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 -algebra and the ideals of bounded -algebra . In addition, we have 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 -algebras, we examine the relationship between Stonean triangle bounded -algebras and Stonean triangle ideals. Finally, we investigate the interrelationships among these various types of triangle ideals. |
| Key words: triangle bounded -algebra Stonean triangle bounded -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: |
| 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 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 -algebra and the ideals of bounded -algebra . In addition, we have 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 -algebras, we examine the relationship between Stonean triangle bounded -algebras and Stonean triangle ideals. Finally, we investigate the interrelationships among these various types of triangle ideals. |
