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On Injective MV-Modules

dc.contributor.authorBorzooei, Rajabali A.
dc.contributor.authorGoraghani, S. Saidi
dc.date.accessioned2019-05-24T07:15:59Z
dc.date.available2019-05-24T07:15:59Z
dc.date.issued2018
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/28483
dc.description.abstractIn this paper, by considering the notion of MV-module, which is the structure that naturally correspond to lu-modules over lu-rings, we study injective MV-modules and we investigate some conditions for constructing injective MV-modules. Then we define the notions of essential A-homomorphisms and essential extension of A-homomorphisms, where A is a product MV-algebra, and we get some of there properties. Finally, we prove that a maximal essential extension of any A-ideal of an injective MV-module is an injective A-module, too.en_GB
dc.language.isoenen_GB
dc.publisherWydawnictwo Uniwersytetu Łódzkiegoen_GB
dc.relation.ispartofseriesBulletin of the Section of Logic; 4
dc.rightsThis work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.en_GB
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0en_GB
dc.subject(MV, PMV)-algebraen_GB
dc.subjectMV-moduleen_GB
dc.subjectInjective MV-moduleen_GB
dc.subjectEssential extensionen_GB
dc.titleOn Injective MV-Modulesen_GB
dc.typeArticleen_GB
dc.page.number283-298
dc.contributor.authorAffiliationShahid Beheshti University, Department of Mathematics
dc.contributor.authorAffiliationFarhangian University, Department of Mathematics
dc.identifier.eissn2449-836X
dc.references[1] R. A. Borzooei, S. Saidi Goraghani, Free MV-modules, Journal of Intelligent and Fuzzy System 31(1) (2016), pp. 151–161.en_GB
dc.references[2] C. C. Chang, Algebraic analysis of many-valued logic, Transactions of the American Mathematical Society 88 (1958), pp. 467–490.en_GB
dc.references[3] R. Cignoli, I. M. L. D,Ottaviano, D. Mundici, Algebraic Foundations of Many-valued Reasoning, Kluwer Academic, Dordrecht, (2000).en_GB
dc.references[4] A. Di Nola, A. Dvurecenskij, Product MV-algebras,Multiple-Valued Logics 6 (2001), pp. 193–215.en_GB
dc.references[5] A. Di Nola, P. Flondor, I. Leustean, MV-modules, Journal of Algebra 267 (2003), pp. 21–40.en_GB
dc.references[6] A. Dvurecenskij, On Partial addition in Pseudo MV-algebras, Proceedings of the Fourth International Symposium on Economic Informatics (1999), pp. 952–960.en_GB
dc.references[7] F. Forouzesh, E. Eslami, A. Borumand Saeid, On Prime A-ideals in MV-modules, University Politechnica of Bucharest Scientific Bulletine 76 (2014), pp. 181–198.en_GB
dc.references[8] S. Saidi Goraghani, R. A. Borzooei, Injective MV-modules, Presented at 6th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS), (2018), Kerman, Iran.en_GB
dc.references[9] S. Saidi Goraghani, R. A. Borzooei, Prime ·-Ideals and Fuzzy Prime ·-Ideals in PMV-algebras, Annals of Fuzzy Mathematics and Informatics 12(4) (2016), pp. 527–538.en_GB
dc.references[10] S. Saidi Goraghani, R. A. Borzooei, Results on Prime Ideals in PMV-algebras and MV-modules, Italian Journal of Pure and Applied Mathematics 37 (2017), pp. 183–196.en_GB
dc.contributor.authorEmailborzooei@sbu.ac.ir
dc.contributor.authorEmailsiminsaidi@yahoo.com
dc.identifier.doi10.18778/0138-0680.47.4.04
dc.relation.volume47en_GB
dc.subject.jel06D35en_GB
dc.subject.jel06F99en_GB
dc.subject.jel16D80en_GB


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This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
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