Chain conditions on BL-algebras

The aim of this paper is to solve the open problem appeared in Motamed and Moghaderi (Soft Comput 2012 ), about the relation between Noetherian (Artinian) BL -algebras in short exact sequences. Also, a better theorem to improve its results is suggested. The relation between Noetherian and Artinian B...

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Bibliographic Details
Published inSoft computing (Berlin, Germany) Vol. 18; no. 3; pp. 419 - 426
Main Author Zahiri, O.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2014
Springer Nature B.V
Subjects
Algebra
Artificial Intelligence
Computational Intelligence
Control
Engineering
Foundations
Logic
Mathematical Logic and Foundations
Mechatronics
Robotics
algebra
Sequence
Maximal filter
Length
Prime filter
Noetherian (Artinian)
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Summary:The aim of this paper is to solve the open problem appeared in Motamed and Moghaderi (Soft Comput 2012 ), about the relation between Noetherian (Artinian) BL -algebras in short exact sequences. Also, a better theorem to improve its results is suggested. The relation between Noetherian and Artinian BL -algebras is found, the concept of length for a filter in BL -algebras is introduced and properties of finite length BL -algebras are developed. Finally, it is proved that any BL -algebra has finite length if and only if be Noetherian and Artinian.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-013-1099-2