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On the structure of hoops

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Abstract.

A hoop is a naturally ordered pocrim (i.e., a partially ordered commutative residuated integral monoid). We list some basic properties of hoops, describe in detail the structure of subdirectly irreducible hoops, and establish that the class of hoops, which is a variety, is generated, as a quasivariety, by its finite members.

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Authors and Affiliations

  1. Department of Mathemaática, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, , , , , , PT

    W. J. Blok

  2. Centro de Álgebra, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal, , , , , , PT

    I. M. A. Ferreirim

Authors
  1. W. J. Blok
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  2. I. M. A. Ferreirim
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Received January 22, 1997; accepted in final form October 31, 1999.

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Blok, W., Ferreirim, I. On the structure of hoops. Algebra univers. 43, 233–257 (2000). https://doi.org/10.1007/s000120050156

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  • DOI: https://doi.org/10.1007/s000120050156

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