Studying the Theory of Hoops Through Some Type of Filters

Gezahagne Mulat Addis and Terefe Getachew Beyene

Journal of Applied Mathematics, 2025, vol. 2025, 1-14

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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:1357590

DOI: 10.1155/jama/1357590

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