On Injective MV-Modules

• Autorzy: Rajabali A. Borzooei , S. Saidi Goraghani
• Języki publikacji: EN

Abstrakty

EN

In 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.

Słowa kluczowe

EN

(MV, PMV)-algebra; MV-module; injective MV-module; essential extension

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2018
• Tom: 47
• Numer: 4

Daty

wydano

2018-12-30

Twórcy

autor

Rajabali A. Borzooei

• Shahid Beheshti University, Department of Mathematics

autor

S. Saidi Goraghani

• Farhangian University, Department of Mathematics

Bibliografia

• R. A. Borzooei, S. Saidi Goraghani, Free MV-modules, Journal of Intelligent and Fuzzy System 31(1) (2016), pp. 151–161.
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• A. Di Nola, A. Dvurečenskij, Product MV-algebras,Multiple-Valued Logics 6 (2001), pp. 193–215.
• A. Di Nola, P. Flondor, I. Leustean, MV-modules, Journal of Algebra 267 (2003), pp. 21–40.
• A. Dvurečenskij, On Partial addition in Pseudo MV-algebras, Proceedings of the Fourth International Symposium on Economic Informatics (1999), pp. 952–960.
• 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.
• S. Saidi Goraghani, R. A. Borzooei, Injective MV-modules, Presented at 6th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS), (2018), Kerman, Iran.
• 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.
• 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.

Identyfikatory

DOI

10.18778/0138-0680.47.4.04