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On semiconic idempotent commutative residuated lattices

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In this paper, we study semiconic idempotent commutative residuated lattices. An algebra of this kind is a semiconic generalized Sugihara monoid if it is generated by the lower bounds of the monoid identity. We establish a category equivalence between semiconic generalized Sugihara monoids and Brouwerian algebras with a strong nucleus. As an application, we show that central semiconic generalized Sugihara monoids are strongly amalgamable.

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Acknowledgements

The author is extremely grateful to the referees for their careful reading and valuable suggestions which lead to a substantial improvement of this paper. In particular, Theorem 3.3 is due to a referee. Supported by the Institute of Meteorological Big Data-Digital Fujian and Fujian Key Laboratory of Data Science and Statistics.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, 363000, Fujiang, People’s Republic of China

    Wei Chen

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  1. Wei Chen
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Correspondence to Wei Chen.

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Communicated by J. G. Raftery.

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The research of the author was supported by grants of the NSF of China # 11171294, China # 11571158, Fujian Province # 2014J01019.

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Chen, W. On semiconic idempotent commutative residuated lattices. Algebra Univers. 81, 36 (2020). https://doi.org/10.1007/s00012-020-00666-6

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  • DOI: https://doi.org/10.1007/s00012-020-00666-6

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