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Variety generated by conical residuated lattice-ordered idempotent monoids

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Abstract

In this paper, we study the variety generated by conical idempotent residuated lattices. After obtaining some properties of conical idempotent residuated lattices, we establish a chain decomposition theorem for conical idempotent residuated lattices and give an equational basis for the variety. It is proved that the variety has the finite embeddability property. It is also proved that the semigroup reduct of a semiconical idempotent residuated lattice is a regular band.

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Acknowledgements

The authors would like to thank the referee heartily for his/her careful reading and valuable suggestions which lead to a substantial improvement of this paper.

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Authors and Affiliations

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

    Wei Chen

  2. Department of Mathematics, Huizhou University, Huizhou, 516007, Guangdong, People’s Republic of China

    Yizhi Chen

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  1. Wei Chen
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  2. Yizhi Chen
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Correspondence to Wei Chen.

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Communicated by Jimmie D. Lawson.

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This work is supported by Grants of the NSF of China #11171294, China #11571158, Fujian Province #2014J01019, Guangdong Province #2014A030310119; and by the outstanding Young Innovative Talent Training Project in Guangdong Universities #2013LYM0086.

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Chen, W., Chen, Y. Variety generated by conical residuated lattice-ordered idempotent monoids. Semigroup Forum 98, 431–455 (2019). https://doi.org/10.1007/s00233-019-10014-3

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  • DOI: https://doi.org/10.1007/s00233-019-10014-3

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