Zariski topology on the spectrum of fuzzy classical primary submodules

Phakakorn Panpho; Pairote Yiarayong

doi:10.4995/agt.2022.17427

Authors

Phakakorn Panpho Pibulsongkram Rajabhat University
Pairote Yiarayong Pibulsongkram Rajabhat University https://orcid.org/0000-0003-1525-9536

DOI:

https://doi.org/10.4995/agt.2022.17427

Keywords:

Zariski topology, classical primary submodule, fuzzy classical primary submodule, fuzzy classical primary spectrum, fuzzy primary ideal

Abstract

Let R be a commutative ring with identity and M a unitary R-module. The fuzzy classical primary spectrum F cp.spec(M) is the collection of all fuzzy classical primary submodules A of M, the recent generalization of fuzzy primary ideals and fuzzy classical prime submodules. In this paper, we topologize FM(M) with a topology having the fuzzy primary Zariski topology on the fuzzy classical primary spectrum F cp.spec(M) as a subspace topology, and investigate the properties of this topological space.

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Author Biographies

Phakakorn Panpho, Pibulsongkram Rajabhat University

Major of Physics, Faculty of Science and Technology

Pairote Yiarayong, Pibulsongkram Rajabhat University

Department of Mathematics, Faculty of Science and Technology

References

J. Abuhlail, A Zariski topology for modules, Communications in Algebra 39 (2011), 4163-4182. https://doi.org/10.1080/00927872.2010.519748

M. Alkan and Y. Tiras, Projective modules and prime submodules, Czechoslovak Math. J. 56 (2006), 601-611. https://doi.org/10.1007/s10587-006-0041-5

R. Ameri and R. Mahjoob, Spectrum of prime $L$-submodules, Fuzzy Sets Syst. 159 (2008), 1107-1115. https://doi.org/10.1016/j.fss.2007.08.011

R. Ameri and R. Mahjoob, Spectrum of prime fuzzy hyperideals, Iranian Journal of Fuzzy Systems 6, no. 4 (2009), 61-72.

R. Ameri and R. Mahjoob, Some topological properties of spectrum of fuzzy submodules, Iranian Journal of Fuzzy Systems 14, no. 1 (2017), 77-87.

R. Ameri, R. Mahjoob and M. Mootamani, The Zariski topology on the spectrum of prime L-submodules, Soft Comput. 12 (2008), 901-908. https://doi.org/10.1007/s00500-007-0259-7

A. Azizi, Prime submodules and flat modules, Acta Math. Sin. (Eng. Ser.) 23 (2007), 47-152. https://doi.org/10.1007/s10114-005-0813-0

J. Castro, J. Rios and G. Tapia, Some aspects of Zariski topology for multiplication modules and their attached frames and quantales, J. Korean Math. Soc. 56, no. 5 (2019), 1285-1307.

J. Dauns, Prime modules, J. Reine Angew Math. 298 (1978), 156-181. https://doi.org/10.1515/crll.1978.298.156

A. Y. Darani and S. Motmaen, Zariski topology on the spectrum of graded classical prime submodules, Appl. Gen. Topol. 14, no. 2 (2013), 159-169. https://doi.org/10.4995/agt.2013.1586

J. Goswami and H. K. Saikia, On the spectrum of weakly prime submodule, Thai Journal of Mathematics 19, no. 1 (2021), 51-58.

W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets Syst. 8 (1982), 133-139. https://doi.org/10.1016/0165-0114(82)90003-3

C. P. Lu, The Zariski topology on the prime spectrum of a module, Houston J. Math. 25 (1999), 417-432.

C. V. Negoita and D. A. Ralescu, Application of fuzzy systems analysis, Birkhauser, Basel, 1975. https://doi.org/10.1007/978-3-0348-5921-9

H. A. Toroghy and S. S. Pourmortazavi, On the prime spectrum of modules, Miskolc Mathematical Notes 16, no. 2 (2015), 1233-1242. https://doi.org/10.18514/MMN.2015.1102

H. A. Toroghy and R. O. Sarmazdeh, On the prime spectrum of a module and Zariski topologies, Communications in Algebra 38 (2010), 4461-4475. https://doi.org/10.1080/00927870903386510

L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X

K. A. Zoubi and M. Jaradat, The Zariski topology on the graded classical prime spectrum of a graded module over a graded commutative ring, Matematicki Vesnik 70, no. 4 (2018), 303-313.