L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras
In this paper, we apply the concept of fuzzy sets to Novikov algebras, and introduce the concepts of L-fuzzy ideals and L-fuzzy subalgebras. We get a sufficient and neccessary condition such that an L-fuzzy subspace is an L-fuzzy ideal. Moreover, we show that the quotient algebra A/μ of the L-fuzzy...
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| Format: | Article |
| Language: | English |
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De Gruyter
2019-12-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2019-0126 |
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doaj-7e394200d05d4e99b9fdf7fc79218b2e2021-09-06T19:20:11ZengDe GruyterOpen Mathematics2391-54552019-12-011711538154610.1515/math-2019-0126math-2019-0126L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebrasZhou Xin0Chen Liangyun1Chang Yuan2School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, ChinaSchool of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, ChinaSchool of Mathematics, Dongbei University of Finance and Economics, Dalian, 116025, ChinaIn this paper, we apply the concept of fuzzy sets to Novikov algebras, and introduce the concepts of L-fuzzy ideals and L-fuzzy subalgebras. We get a sufficient and neccessary condition such that an L-fuzzy subspace is an L-fuzzy ideal. Moreover, we show that the quotient algebra A/μ of the L-fuzzy ideal μ is isomorphic to the algebra A/Aμ of the non-fuzzy ideal Aμ. Finally, we discuss the algebraic properties of surjective homomorphic image and preimage of an L-fuzzy ideal.https://doi.org/10.1515/math-2019-0126fuzzy setfuzzy algebrafuzzy subalgebrafuzzy ideal03e7208a72 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Zhou Xin Chen Liangyun Chang Yuan |
| spellingShingle |
Zhou Xin Chen Liangyun Chang Yuan L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras Open Mathematics fuzzy set fuzzy algebra fuzzy subalgebra fuzzy ideal 03e72 08a72 |
| author_facet |
Zhou Xin Chen Liangyun Chang Yuan |
| author_sort |
Zhou Xin |
| title |
L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras |
| title_short |
L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras |
| title_full |
L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras |
| title_fullStr |
L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras |
| title_full_unstemmed |
L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras |
| title_sort |
l-fuzzy ideals and l-fuzzy subalgebras of novikov algebras |
| publisher |
De Gruyter |
| series |
Open Mathematics |
| issn |
2391-5455 |
| publishDate |
2019-12-01 |
| description |
In this paper, we apply the concept of fuzzy sets to Novikov algebras, and introduce the concepts of L-fuzzy ideals and L-fuzzy subalgebras. We get a sufficient and neccessary condition such that an L-fuzzy subspace is an L-fuzzy ideal. Moreover, we show that the quotient algebra A/μ of the L-fuzzy ideal μ is isomorphic to the algebra A/Aμ of the non-fuzzy ideal Aμ. Finally, we discuss the algebraic properties of surjective homomorphic image and preimage of an L-fuzzy ideal. |
| topic |
fuzzy set fuzzy algebra fuzzy subalgebra fuzzy ideal 03e72 08a72 |
| url |
https://doi.org/10.1515/math-2019-0126 |
| work_keys_str_mv |
AT zhouxin lfuzzyidealsandlfuzzysubalgebrasofnovikovalgebras AT chenliangyun lfuzzyidealsandlfuzzysubalgebrasofnovikovalgebras AT changyuan lfuzzyidealsandlfuzzysubalgebrasofnovikovalgebras |
| _version_ |
1717777080904581120 |