Abstract
Let R be a commutative ring with identity and let M be an R-module. We topologize L − Spec(M), the collection of all prime L-submodules of M, analogous to that for FSpec(R), the spectrum of fuzzy prime ideals of R, and investigate the properties of this topological space. In particular, we will study the relationship between L − Spec(M) and L − Spec(R/Ann(M)) and obtain some results.
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References
Bhambri SK, Kumar R and Kumar P (1993). Fuzzy prime submodules and radical of a fuzzy submodules. Bull Cal Math Soc 87: 163–168
Dixit VN, Kummar R and Ajmal N (1991). Fuzzy ideals and fuzzy prime ideals of a ring. Fuzzy Sets Syst 44: 127–138
Goguen JA (1967). L-fuzzy Sets. J Math Appl 18: 145–174
Hadji-Abadi H and Zahedi MM (1996). Some results on fuzzy prime spectrum of a ring. Fuzzy Sets Syst 77: 235–240
Kumar R (1992). Fuzzy prime spectrum of a ring. Fuzzy Sets Syst 46: 147–154
Kumar R and Kohli JK (1993). Fuzzy prime spectrum of a ring II. Fuzzy Sets Syst 59: 223–230
Kumbhojkar HV (1994). Spectrum of prime fuzzy ideals. Fuzzy Sets Syst 62: 101–109
Kumbhojkar HV (1997). Some comments on spectrum of prime fuzzy ideals of a ring. Fuzzy Sets Syst 85: 109–114
Lu CP (1987). Prime submodules of modules. Comm Math Univ 33: 61–69
Lu CP (1995). Spectra of modules. Commun Algebra 23(10): 3741–3752
Lu CP (1999). The Zariski topology on the spectrum of a modules. Houst J Math 25(3): 417–432
McCasland RL, Moore ME and Smith PF (1997). On the spectrum of modules over a commutative ring. Commun Algebra 25(1): 79–103
Mordeson JN, Malik DS (1998) Fuzzy commutative algebra. World Scientific Publishing Co. Pet. Ltd
Mukherjee TK and Sen MK (1987). On fuzzy ideals of a ring I. Fuzzy Sets Syst 21: 99–104
Negoita CV and Ralescu DA (1975). Application of fuzzy systems analysis. Birkhauser, Basel
Pan F-Z (1987). Fuzzy finitely generated modules. Fuzzy Sets Syst 21: 105–113
Rosenfeld R (1971). Fuzzy groups. J Math Anal Appl 35: 512–517
Sidky FI (2001). On radical of fuzzy submodules and primary fuzzy submodules. Fuzzy Sets Syst 119: 419–425
Zadeh LA (1965). Fuzzy sets. Inform Control 8: 338–353
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Ameri, R., Mahjoob, R. & Mootamani, M. The Zariski topology on the spectrum of prime L-submodules. Soft Comput 12, 901–908 (2008). https://doi.org/10.1007/s00500-007-0259-7
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DOI: https://doi.org/10.1007/s00500-007-0259-7