On Injective MV-Modules

Rajabali A. Borzooei; S. Saidi Goraghani

doi:10.18778/0138-0680.47.4.04

Authors

Rajabali A. Borzooei Shahid Beheshti University, Department of Mathematics Author
S. Saidi Goraghani Farhangian University, Department of Mathematics Author

DOI:

https://doi.org/10.18778/0138-0680.47.4.04

Keywords:

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

Abstract

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.

References

R. A. Borzooei, S. Saidi Goraghani, Free MV-modules, Journal of Intelligent and Fuzzy System 31(1) (2016), pp. 151–161.

C. C. Chang, Algebraic analysis of many-valued logic, Transactions of the American Mathematical Society 88 (1958), pp. 467–490.

R. Cignoli, I. M. L. D,Ottaviano, D. Mundici, Algebraic Foundations of Many-valued Reasoning, Kluwer Academic, Dordrecht, (2000).

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.