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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| Published in | Soft computing (Berlin, Germany) Vol. 27; no. 17; pp. 11961 - 11971 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.09.2023
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
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| 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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| AbstractList | 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. |
| Author | Borzooei, R. A. Ahn, S. S. Kologani, M. Aaly |
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| Keywords | Prime ideal Hoop Product of ideals Maximal ideal Nilpotent ideal |
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| References | Namdar, Borzooei, Borumand Saeid, Aaly Kologani (CR11) 2017; 32 CR2 Borzooei, Aaly Kologani (CR4) 2015; 29 Bosbach (CR9) 1970; 69 Borzooei, Aaly Kologani (CR5) 2020; 1 Xie, Liu (CR12) 2020; 1 Borzooei, Aaly Kologani (CR6) 2020; 2 CR7 Georgescu, Leustean, Preoteasa (CR10) 2005; 11 Belluce, Lettieri, Sessa (CR3) 2001; 11 Aaly Kologani, Borzooei (CR1) 2019; 145 Bosbach (CR8) 1969; 64 8807_CR2 PL Belluce (8807_CR3) 2001; 11 RA Borzooei (8807_CR5) 2020; 1 F Xie (8807_CR12) 2020; 1 B Bosbach (8807_CR8) 1969; 64 M Aaly Kologani (8807_CR1) 2019; 145 8807_CR7 RA Borzooei (8807_CR4) 2015; 29 A Namdar (8807_CR11) 2017; 32 RA Borzooei (8807_CR6) 2020; 2 G Georgescu (8807_CR10) 2005; 11 B Bosbach (8807_CR9) 1970; 69 |
| References_xml | – ident: CR7 – volume: 1 start-page: 61 issue: 1 year: 2020 end-page: 77 ident: CR5 article-title: Results on hoops publication-title: J Algebraic Hyperstruct Log Algebras doi: 10.29252/hatef.jahla.1.1.5 contributor: fullname: Aaly Kologani – volume: 69 start-page: 1 year: 1970 end-page: 14 ident: CR9 article-title: Komplementäre halbgruppen publication-title: Kongruenzen and quotienten, Fundam Math doi: 10.4064/fm-69-1-1-14 contributor: fullname: Bosbach – volume: 32 start-page: 1805 year: 2017 end-page: 1813 ident: CR11 article-title: Some results in hoop algebras publication-title: J Intell Fuzzy Syst doi: 10.3233/JIFS-152553 contributor: fullname: Aaly Kologani – ident: CR2 – volume: 2 start-page: 109 issue: 3 year: 2020 end-page: 120 ident: CR6 article-title: Minimal prime ideals in hoops publication-title: J Algebraic Hyperstruct Log Algebras doi: 10.52547/HATEF.JAHLA.2.3.9 contributor: fullname: Aaly Kologani – volume: 11 start-page: 153 issue: 1–2 year: 2005 end-page: 184 ident: CR10 article-title: Pseudo-hoops publication-title: J Multiple Valued logic Soft Comput contributor: fullname: Preoteasa – volume: 145 start-page: 1 issue: 2 year: 2019 end-page: 22 ident: CR1 article-title: On ideal theory of hoop algebras publication-title: Math Bohem contributor: fullname: Borzooei – volume: 29 start-page: 223 year: 2015 end-page: 234 ident: CR4 article-title: Local and perfect semihoops publication-title: J Intell Fuzzy Syst doi: 10.3233/IFS-151589 contributor: fullname: Aaly Kologani – volume: 64 start-page: 257 year: 1969 end-page: 287 ident: CR8 article-title: Komplementäre halbgruppen publication-title: Axiomatik arithmetik, Fundam Math doi: 10.4064/fm-64-3-257-287 contributor: fullname: Bosbach – volume: 11 start-page: 341 issue: 3–4 year: 2001 end-page: 350 ident: CR3 article-title: Products of ideals in MV-algebras publication-title: J Appl Non Class Logics doi: 10.3166/jancl.11.341-350 contributor: fullname: Sessa – volume: 1 start-page: 39 issue: 4 year: 2020 end-page: 53 ident: CR12 article-title: Ideals in pseudo-hoop algebras publication-title: J Algebraic Hyperstruct Logic Algebras doi: 10.52547/HATEF.JAHLA.1.4.3 contributor: fullname: Liu – volume: 11 start-page: 153 issue: 1–2 year: 2005 ident: 8807_CR10 publication-title: J Multiple Valued logic Soft Comput contributor: fullname: G Georgescu – volume: 32 start-page: 1805 year: 2017 ident: 8807_CR11 publication-title: J Intell Fuzzy Syst doi: 10.3233/JIFS-152553 contributor: fullname: A Namdar – volume: 145 start-page: 1 issue: 2 year: 2019 ident: 8807_CR1 publication-title: Math Bohem contributor: fullname: M Aaly Kologani – ident: 8807_CR2 – volume: 69 start-page: 1 year: 1970 ident: 8807_CR9 publication-title: Kongruenzen and quotienten, Fundam Math doi: 10.4064/fm-69-1-1-14 contributor: fullname: B Bosbach – volume: 1 start-page: 61 issue: 1 year: 2020 ident: 8807_CR5 publication-title: J Algebraic Hyperstruct Log Algebras doi: 10.29252/hatef.jahla.1.1.5 contributor: fullname: RA Borzooei – volume: 64 start-page: 257 year: 1969 ident: 8807_CR8 publication-title: Axiomatik arithmetik, Fundam Math doi: 10.4064/fm-64-3-257-287 contributor: fullname: B Bosbach – volume: 2 start-page: 109 issue: 3 year: 2020 ident: 8807_CR6 publication-title: J Algebraic Hyperstruct Log Algebras doi: 10.52547/HATEF.JAHLA.2.3.9 contributor: fullname: RA Borzooei – volume: 11 start-page: 341 issue: 3–4 year: 2001 ident: 8807_CR3 publication-title: J Appl Non Class Logics doi: 10.3166/jancl.11.341-350 contributor: fullname: PL Belluce – volume: 29 start-page: 223 year: 2015 ident: 8807_CR4 publication-title: J Intell Fuzzy Syst doi: 10.3233/IFS-151589 contributor: fullname: RA Borzooei – ident: 8807_CR7 doi: 10.1007/s00500-022-07193-7 – volume: 1 start-page: 39 issue: 4 year: 2020 ident: 8807_CR12 publication-title: J Algebraic Hyperstruct Logic Algebras doi: 10.52547/HATEF.JAHLA.1.4.3 contributor: fullname: F Xie |
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| SubjectTerms | Algebra Algebraic Analytical Methods in Soft Computing Artificial Intelligence Computational Intelligence Control Engineering Foundation Hoops Mathematical Logic and Foundations Mathematicians Mechatronics Robotics |
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| Title | Product of ideals in hoops |
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