Lifting Elements in Coherent Quantales
Subject Areas : Transactions on Fuzzy Sets and Systems
1 - Department of Computer Science, Faculty of Mathematics and Informatics, Bucharest University, Bucharest, Romania.
Keywords:
Abstract :
[1] M. Aghajani and A. Tarizadeh, Characterization of Gelfand rings, specially of clean rings and their dual rings, Results Math., 75(3) (2020) 75-125.
[2] M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley Publ. Comp., (1969).
[3] R. Balbes and Ph. Dwinger, Distributive Lattices, Univ. of Missouri Press, (1974).
[4] B. Banaschewski, Gelfand and exchange rings: Their spectra in point free topology, Arab. J. Sci. Eng., 25(2C) (2000), 3-22.
[5] B. Barania Nia and A. Borumand Saeid, Classes of pseudo BL-algebras in view of right Boolean lifting property, Transactions of A. Razmadze Mathematical Institute, 172 (2018), 146-163.
[6] B. Barania Nia and A. Borumand Saeid, Study of pseudo BL-algebras in view of right Boolean lifting property, Appl. Appl. Math., 13(1) (2018), 354-381.
[7] G. Birkhoff, Lattice Theory, AMS Collocquium Publ., (1967).
[8] D. Cheptea, Lifting properties in classes of universal algebras, Ph. D. Thesis, In preparation.
[9] D. Cheptea, G. Georgescu and C. Muresan, Boolean lifting properties for bounded distributive lattices, Sci. Ann. Comput. Sci., 25 (2015), 29-67.
[10] D. Cheptea and G. Georgescu, Boolean lifting properties in quantales, Soft Computing, 24 (2020), 1-13.
[11] T. Demba, On the hull-kernel and inverse topology on frames, Algebra Universalis, 70 (2013), 197-212.
[12] M. Dickmann, N. Schwarz and M. Tressl, Spectral Spaces, Cambridge University Press, (2019).
[13] P. Eklund, J. G. Garcia, U. Hohle and J. Kortelainen, Semigroups in Complete Lattices: Quantales, Modules and Related Topics, Springer USA, (2018).
[14] A. Facchini, C. A. Pinocchiaro and G. Janelidze, Abstractly constructed prime spectra, Algebra Universalis, 83(8) (2022). Available online: https://doi.org/10.107/s00012-021-00764-z.
[15] N. Galatos, P. Jipsen, T. Kowalski and H. Ono, Residuated Lattices: An Algebraic Glimpse at Structural Logics, Studies in Logic and The Foundation of Mathematics, 151, Elsevier, USA, (2007).
[16] G. Georgescu, The reticulation of a quantale, Rev. Roumaine Math. Pures Appl., 40(7-8) (1995), 619-631.
[17] G. Georgescu, D. Cheptea and C. Muresan, Algebraic and topological results on lifting properties in residuated lattices, Fuzzy Sets Systems, 271 (2015), 102-132.
[18] G. Georgescu, L. Leustean and C. Muresan, Maximal residuated lattices with lifting Boolean center, Algebra Universalis, 63 (2010), 83-99.
[19] G. Georgescu and C. Muresan, Boolean lifting property for residuated lattices, Soft Computing, 18 (2014), 2075-2089.
[20] G. Georgescu and C. Muresan, Congruence Boolean Lifting Property, J. Multiple-valued Logic and Soft Computing, 29 (2017), 225-274.
[21] G. Georgescu and C. Muresan, Factor Congruence Lifting Property, Studia Logica, 225 (2017), 1079-2017.
[22] G. Georgescu, L. Kwuida and C. Muresan, Functorial properties of the reticulation of a universal algebra, J. Applied Logic, 8(5) (2021), 1123-1168.
[23] G. Georgescu, Some classes of quantale morphisms, J. Algebra Number Theory Appl., 24(2) (2021), 111-153.
[24] G. Georgescu, Flat topology on the spectra of quantales, Fuzzy Sets and Systems, 406 (2021), 22-41.
[25] G. Georgescu, Reticulation of a quantale, pure elements and new transfer properties, Fuzzy Sets and Systems, (2021). Available online: https://doi.org/10.1016/j.fss.2021.06.003.
[26] G. Georgescu, New results on Congruence Boolean Lifting Property, Journal of Algebraic Hyperstructures and Logical Algebras, 3(1) (2022), 15-34.
[27] A. W. Hager, C. M. Kimber and W. Wm McGovern, Clean unital l-groups, Math. Slovaca, 63 (2013), 979-992.
[28] M. Hochster, Prime ideals structures in commutative rings, Trans. Amer. Math. Soc., 142 (1969), 43-60.
[29] P. Jipsen, Generalization of Boolean products for lattice-ordered algebras, Annals Pure Appl. Logic, 161 (2009), 224-234.
[30] P. T. Johnstone, Stone Spaces, Cambridge University Press, (1982).
[31] A. J. de Jong et al., Stacs project. Available online: http://stacs.math.columbia.edu.
[32] N. A. Kermani, E. Eslami and A. Borumand Saeid, Central lifting property for orthomodular lattices, Math. Slovaca, 70(6) (2020), 1307-1316.
[33] L. Leustean, Representations of Many-valued Algebras, Editura Universitara, Bucharest, (2010).
[34] J. Martinez, Abstract ideal theory, Ordered Algebraic Structures, Lecture Notes in Pure and Appl. Math., 99, Marcel Dekker, New York, (1985).
[35] C. Muresan, Algebras of many-valued logic, Ph. D. Thesis, Bucharest University, (2009).
[36] W. K. Nicholson, Lifting idempotents and exchange rings, Transaction of A.M.S., 229 (1977), 278-288.
[37] J. Paseka, Regular and normal quantales, Arch. Math. (Brno), 22 (1996), 203-210.
[38] J. Paseka and J. Rosicky, Quantales, Current Research in Operational Quantum Logic : Algebras, Categories and Languages, Fund. Theories Phys, vol. 111, Kluwer Acad. Publ., Dordrecht, (2000), 245-262.
[39] J. Picado and A. Pultr, Frames and Locales: Topology without points, Frontiers in Mathematics, Springer, Basel, (2012).
[40] E. Rostami, S. Hedayat, S. Karimzadeh and R. Nekooei, Comaximal factorization of of lifting ideals, J. Algebra Appl., 19(1) (2021). Available online: https://doi.org/10.1142/S021949882250044x.
[41] K. I. Rosenthal, Quantales and Their Applications, Longman Scientific and Technical, (1989).
[42] H. Simmons, Reticulated rings, J. Algebra, 66 (1980), 169-192.
[43] A. Tarizadeh and P.K. Sharma, Structural results on lifting, orthogonality and finiteness of idempotents, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 116(1), 54 (2022).
