References

SOME CLASSES OF QUANTALE MORPHISMS


[1] M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Company, 1969.

[2] R. Balbes and Ph. Dwinger, Distributive Lattices, University of Missouri Press, 1974.

[3] P. Bhattacharjee, Rigid extensions of algebraic frames, Algebra Universalis 62(1) (2010), 133-149.
DOI: https://doi.org/10.1007/s00012-010-0034-y

[4] P. Bhattacharjee, Minimal Prime Element Space of an Algebraic Frame, Dissertation, Bowling Green State University, 2009.

[5] P. Bhattacharjee, K. M. Dress and W. Wm. McGovern, Extensions of commutative rings, Topology and its Applications 158(14) (2011), 1802-1814.
DOI: https://doi.org/10.1016/j.topol.2011.06.015

[6] P. Bhattacharjee, M. A. Moshier and J. Walters-Wayland, Rigid frame maps and Booleanizations, Topology and its Applications 194 (2015), 400-408.
DOI: https://doi.org/10.1016/j.topol.2015.08.021

[7] G. Birkhoff, Lattice Theory, 3rd Edition, Volume 25, AMS Collocquium Publications, 1967.

[8] D. Cheptea and G. Georgescu, Boolean lifting properties in quantales, Soft Computing 24(8) (2020), 6169-6181.
DOI: https://doi.org/10.1007/s00500-020-04752-8

[9] M. Dickmann, N. Schwartz and M. Tressl, Spectral Spaces, Cambridge University Press, 2019.
DOI: https://doi.org/10.1017/9781316543870

[10] D. E. Dobbs, M. Fontana and I. Papick, On the flat spectral topology, Rendiconti di Matematica 1(4) (1981), 559-578.

[11] P. Eklund, J. G. Garcia, U. Hohle and J. Kortelainen, Semigroups in Complete Lattices: Quantales, Modules and Related Topics, Springer, 2018.
DOI: https://doi.org/10.1007/978-3-319-78948-4

[12] 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, 2007.

[13] G. Georgescu, The reticulation of a quantale, Revue Roumaine des Mathematiques Pures et Appliquees 40(7) (1995), 619-631.

[14] G. Georgescu, Flat topology on the spectra of quantales, Fuzzy Sets and Systems 406 (2021), 22-41.
DOI: https://doi.org/10.1016/j.fss.2020.08.009

[15] M. Hochster, Prime ideals structure in commutative rings, Transactions of the American Mathematical Society 142 (1969), 43-60.
DOI: https://doi.org/10.1090/S0002-9947-1969-0251026-X

[16] P. Jipsen, Generalizations of Boolean products for lattice-ordered algebras, Annals of Pure and Applied Logic 161(2) (2009), 228-234.
DOI: https://doi.org/10.1016/j.apal.2009.05.005

[17] P. T. Johnstone, Stone Spaces, Cambridge University Press, 1982.

[18] K. Keimel, A unified theory of minimal prime ideals, Acta Mathematica Academiae Scientiarum Hungarica 23(2) (1972), 51-69.
DOI: https://doi.org/10.1007/BF01889903

[19] J. Martinez, Abstract Ideal Theory: Ordered Algebraic Structures, Lecture Notes in Pure and Applied Mathematics, 99, Marcel Dekker, New York, 1985, pp. 125-138.

[20] E. Matlis, The minimal prime spectrum of a reduced ring, Illinois Journal of Mathematics 27(3) (1983), 353-391.
DOI: https://doi.org/10.1215/ijm/1256046365

[21] J. Paseka and J. Rosicky, Quantales, Current Research in Operational Quantum Logic: Algebras, Categories and Languages, Fundamental Theories of Physics, Vol. 111, Kluwer, 2000, 245-261.

[22] G. Picavet, Ultrafiltres sur une espace spectral: Anneaux de Baer - Anneaux a spectre maximal compacts, Mathematica Scandinavica 46(1) (1980), 23-53.

[23] K. I. Rosenthal, Quantales and their Applications, Longman Scientific and Technical, 1989.

[24] H. Simmons, Reticulated rings, Journal of Algebra 66(1) (1980), 169-192.
DOI: https://doi.org/10.1016/0021-8693(80)90118-0

[25] H. Simmons, An introduction of Idioms, 2014.
http:www.cs.man.ac.uk/~hsimmons/00-IDSandMODS/001I2

[26] T. P. Speed, Spaces of ideals of distributive lattices II: Minimal prime ideals, Journal of the Australian Mathematical Society 18(1) (1974), 54-72.
DOI: https://doi.org/10.1017/S144678870001911X

[27] S. H. Sun, Spectra of monoidal-lattices, Algebra Universalis 31(2) (1994), 274-292.
DOI: https://doi.org/10.1007/BF01236523

[28] A. Tarizadeh, Flat topology and its dual aspects, Communications in Algebra 47(1) (2019), 195-205.
DOI: https://doi.org/10.1080/00927872.2018.1469637

[29] A. Tarizadeh, Zariski compactness of minimal spectrum and flat compactness of maximal spectrum, Journal of Algebra and its Applications 18(11) (2019); Article 1950202.
DOI: https://doi.org/10.1142/S0219498819502025