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Chain conditions on \(\textit{BL}\)-algebras

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Abstract

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) \(\textit{BL}\)-algebras in short exact sequences. Also, a better theorem to improve its results is suggested. The relation between Noetherian and Artinian \(\textit{BL}\)-algebras is found, the concept of length for a filter in \(\textit{BL}\)-algebras is introduced and properties of finite length \(\textit{BL}\)-algebras are developed. Finally, it is proved that any \(\textit{BL}\)-algebra has finite length if and only if be Noetherian and Artinian.

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Authors and Affiliations

  1. Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran

    O. Zahiri

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  1. O. Zahiri
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Correspondence to O. Zahiri.

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Communicated by L. Spada.

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Zahiri, O. Chain conditions on \(\textit{BL}\)-algebras. Soft Comput 18, 419–426 (2014). https://doi.org/10.1007/s00500-013-1099-2

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  • DOI: https://doi.org/10.1007/s00500-013-1099-2

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