Algebraic de Morgan's laws for non-commutative rings
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 36 (1995) no. 2, pp. 127-140. 
@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},
     pages = {127--140},
     publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS},
     volume = {36},
     number = {2},
     year = {1995},
     mrnumber = {1338467},
     zbl = {0830.16021},
     language = {en},
     url = {http://www.numdam.org/item/CTGDC_1995__36_2_127_0/}
}
TY  - JOUR
AU  - Niefield, Susan B.
AU  - Sun, Shu-Hao
TI  - Algebraic de Morgan's laws for non-commutative rings
JO  - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY  - 1995
SP  - 127
EP  - 140
VL  - 36
IS  - 2
PB  - Dunod éditeur, publié avec le concours du CNRS
UR  - http://www.numdam.org/item/CTGDC_1995__36_2_127_0/
LA  - en
ID  - CTGDC_1995__36_2_127_0
ER  - 
%0 Journal Article
%A Niefield, Susan B.
%A Sun, Shu-Hao
%T Algebraic de Morgan's laws for non-commutative rings
%J Cahiers de Topologie et Géométrie Différentielle Catégoriques
%D 1995
%P 127-140
%V 36
%N 2
%I Dunod éditeur, publié avec le concours du CNRS
%U http://www.numdam.org/item/CTGDC_1995__36_2_127_0/
%G en
%F 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) no. 2, pp. 127-140. http://www.numdam.org/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 | Zbl

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

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

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

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

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

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

[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 | Zbl

[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 | Zbl

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

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

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

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

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

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

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