Some results on Noetherian and Artinian BL-algebras

Abstract

In this paper, we obtain some relations between Noetherian and Artinian BL-algebras. Further, we derive some theorems and lemmas for composition series, Artinian BL-argebera, as well as the relations between Noetherian, Artinian and short exact sequences. We further study the Noetherian and Artinian over homomorphism BL-algebras and obtain some new results concerning to the essential deductive systems of BL-algebras.

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Acknowledgement

The authors are extremely grateful to the editor and the referee for his/her valuable comments and helpful suggestions which help to improve the paper.

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Correspondence to Jamal Kazemiasl or Farhad Khaksar Haghani or Shahram Heidarian.

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Kazemiasl, J., Haghani, F.K. & Heidarian, S. Some results on Noetherian and Artinian BL-algebras. Indian J Pure Appl Math 51, 705–715 (2020). https://doi.org/10.1007/s13226-020-0425-5

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Key words

  • Artinian (Noetherian) BL-algebra
  • composition series
  • maximal filter
  • short exact sequence

2010 Mathematics Subject Classification

  • 03G25
  • 03G99
  • 06D99