Abstract
In this paper, first by using ideals in hoops we define a new congruence relation on hoops and we make a new quotient structure. Then, we introduce the concept of product ideal in hoops and investigate some properties of it and study some results about prime and maximal ideals and product of them. By using these notions, we define the concept of nilpotent ideal on hoops and we provide a condition for intersection of all maximal ideals to be nilpotent.
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Borzooei, R.A., Kologani, M.A. & Ahn, S.S. Product of ideals in hoops. Soft Comput 27, 11961–11971 (2023). https://doi.org/10.1007/s00500-023-08807-4
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DOI: https://doi.org/10.1007/s00500-023-08807-4