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Studying the Theory of Hoops Through Some Type of Filters

Author

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  • Gezahagne Mulat Addis
  • Terefe Getachew Beyene

Abstract

It is known that the class of hoops is ideally determined, in the sense that every filter of any hoop H is a 1-class of a unique congruence relation on H. This confirms that every filter in a hoop determines one and only one quotient structure. So, given a hoop H and a filter π of H, it is natural to question ourselves what should be the defining properties of π so that the quotient H/π is a join hoop (respectively, a Wajsberg hoop, cancellative hoop, and an MV-algebra) and what should be the property of π such that H/π is a subdirectly irreducible. In this paper, we answer these questions by introducing some new types of filters in hoops called J-filters, w-filters, MV-filters, c-filters, and completely prime filters, respectively.

Suggested Citation

  • Gezahagne Mulat Addis & Terefe Getachew Beyene, 2025. "Studying the Theory of Hoops Through Some Type of Filters," Journal of Applied Mathematics, Hindawi, vol. 2025, pages 1-14, December.
    • Handle: RePEc:hin:jnljam:1357590
    DOI: 10.1155/jama/1357590
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