Product of ideals in hoops

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. B...

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Bibliographic Details
Published inSoft computing (Berlin, Germany) Vol. 27; no. 17; pp. 11961 - 11971
Main Authors Borzooei, R. A., Kologani, M. Aaly, Ahn, S. S.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2023
Springer Nature B.V
Subjects
Algebra
Algebraic
Analytical Methods in Soft Computing
Artificial Intelligence
Computational Intelligence
Control
Engineering
Foundation
Hoops
Mathematical Logic and Foundations
Mathematicians
Mechatronics
Robotics
Prime ideal
Hoop
Product of ideals
Maximal ideal
Nilpotent ideal
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Summary: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.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-023-08807-4