Algebraic de Morgan's laws for non-commutative rings
Niefield, Susan B. ; Sun, Shu-Hao
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 36 (1995), p. 127-140 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1995-01-01
@article{CTGDC_1995__36_2_127_0,
     author = {Niefield, Susan B. and Sun, Shu-Hao},
     title = {Algebraic de Morgan's laws for non-commutative rings},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {36},
     year = {1995},
     pages = {127-140},
     mrnumber = {1338467},
     zbl = {0830.16021},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_1995__36_2_127_0}
}

Niefield, Susan B.; Sun, Shu-Hao. Algebraic de Morgan's laws for non-commutative rings. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 36 (1995) pp. 127-140. http://gdmltest.u-ga.fr/item/CTGDC_1995__36_2_127_0/

[1] L.P. Belluce, Spectral spaces and non-commutative rings, Comm. in Algebra 19 (1991), 1855-1865. | MR 1121110 | Zbl 0728.16002

[2] T.S. Blythe and M.F. Janowitz, "Residuation Theory", Pergamon Press, 1972. | MR 396359 | Zbl 0301.06001

[3] K.R. Goodearl and R.B. Warfield, Jr, "An Introduction to Noncommutative Noetherian Rings", London Math. Soc. Student Texts 16, 1989. | Zbl 0679.16001

[4] P.T. Johnstone, Conditions related to de Morgan's law, Springer Lecture Notes in Mathematics No. 753, 479-491. | MR 555556 | Zbl 0445.03041

[5] I. Kaplansky, "Rings of Operators", W. A. Benjamin, 1968. | MR 244778 | Zbl 0174.18503

[6] I.G. Macdonald, "Algebraic Geometry: An Introduction to Schemes ", Benjamin, New York, 1968. | MR 238845 | Zbl 0172.22401

[7] M. Larsen and P. Mccarthy, "Multiplicative Theory of Ideals", Pure and Appl. Math. No. 43, Academic Press, 1971. | MR 414528 | Zbl 0237.13002

[8] S.B. Niefield and K.R. Rosenthal, De Morgan's law and the spectrum of a commutative ring, J.Algebra 93 (1985), 169-181. | MR 780490 | Zbl 0562.18005

[9] S.B. Niefield and K.R. Rosenthal, A note on the algebraic de Morgan's law, Cahiers de Top. et Geom. Diff. Cat. 26 (1985), 115-120. | Numdam | MR 794750 | Zbl 0575.13002

[10] S.B. Niefield and K.R. Rosenthal, Constructing locales from quantales, Math. Proc. Camb. Phil. Soc. 104 (1988), 215-234 | MR 948908 | Zbl 0658.06007

[11] K.R. Rosenthal, "Quantales and Their Applications", Pitman Research Notes in Math. 234, Longman Scientific and Technical, 1990. | Zbl 0703.06007

[12] H. Simmons, Reticulated rings, J. Algebra 66 (1980), 169-192. | MR 591251 | Zbl 0462.13002

[13] Shu-Hao Sun, A localic approach to minimal spectra, Math. Proc. of Camb. Philo. Soc. 103 (1988), 47-53. | MR 913449 | Zbl 0645.06011

[14] Shu-Hao Sun, The least multiplicative nucleus of a ring, J. Pure Appl. Algebra 78 (1992), 311-318. | MR 1163283 | Zbl 0791.16019

[15] Shu-Hao Sun, Duality on Compact Prime Ringed Spaces, preprint. | MR 1302117 | Zbl 0821.16045

[16] M. Ward and R. Dilworth, Residuated lattices, Trans. Amer. Math. Soc. 45 (1930), 335-354. | JFM 65.0084.01 | MR 1501995