Algebraic de Morgan's laws for non-commutative rings

Susan B. Niefield; Shu-Hao Sun

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1995)

  • Volume: 36, Issue: 2, page 127-140
  • ISSN: 1245-530X

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Niefield, Susan B., and Sun, Shu-Hao. "Algebraic de Morgan's laws for non-commutative rings." Cahiers de Topologie et Géométrie Différentielle Catégoriques 36.2 (1995): 127-140. <http://eudml.org/doc/91561>.

@article{Niefield1995,
author = {Niefield, Susan B., Sun, Shu-Hao},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {strong extremal disconnectedness; spectra; non-commutative rings},
language = {eng},
number = {2},
pages = {127-140},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Algebraic de Morgan's laws for non-commutative rings},
url = {http://eudml.org/doc/91561},
volume = {36},
year = {1995},
}

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
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 36
IS - 2
SP - 127
EP - 140
LA - eng
KW - strong extremal disconnectedness; spectra; non-commutative rings
UR - http://eudml.org/doc/91561
ER -

References

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  1. [1] L.P. Belluce, Spectral spaces and non-commutative rings, Comm. in Algebra19 (1991), 1855-1865. Zbl0728.16002MR1121110
  2. [2] T.S. Blythe and M.F. Janowitz, "Residuation Theory", Pergamon Press, 1972. Zbl0301.06001MR396359
  3. [3] K.R. Goodearl and R.B. Warfield, Jr, "An Introduction to Noncommutative Noetherian Rings", London Math. Soc. Student Texts16, 1989. Zbl0679.16001
  4. [4] P.T. Johnstone, Conditions related to de Morgan's law, Springer Lecture Notes in Mathematics No. 753, 479-491. Zbl0445.03041MR555556
  5. [5] I. Kaplansky, "Rings of Operators", W. A. Benjamin, 1968. Zbl0174.18503MR244778
  6. [6] I.G. MacDonald, "Algebraic Geometry: An Introduction to Schemes ", Benjamin, New York, 1968. Zbl0172.22401MR238845
  7. [7] M. Larsen and P. McCarthy, "Multiplicative Theory of Ideals", Pure and Appl. Math. No. 43, Academic Press, 1971. Zbl0237.13002MR414528
  8. [8] S.B. Niefield and K.R. Rosenthal, De Morgan's law and the spectrum of a commutative ring, J.Algebra93 (1985), 169-181. Zbl0562.18005MR780490
  9. [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. Zbl0575.13002MR794750
  10. [10] S.B. Niefield and K.R. Rosenthal, Constructing locales from quantales, Math. Proc. Camb. Phil. Soc.104 (1988), 215-234 Zbl0658.06007MR948908
  11. [11] K.R. Rosenthal, "Quantales and Their Applications", Pitman Research Notes in Math. 234, Longman Scientific and Technical, 1990. Zbl0703.06007
  12. [12] H. Simmons, Reticulated rings, J. Algebra66 (1980), 169-192. Zbl0462.13002MR591251
  13. [13] Shu-Hao Sun, A localic approach to minimal spectra, Math. Proc. of Camb. Philo. Soc.103 (1988), 47-53. Zbl0645.06011MR913449
  14. [14] Shu-Hao Sun, The least multiplicative nucleus of a ring, J. Pure Appl. Algebra78 (1992), 311-318. Zbl0791.16019MR1163283
  15. [15] Shu-Hao Sun, Duality on Compact Prime Ringed Spaces, preprint. Zbl0821.16045MR1302117
  16. [16] M. Ward and R. Dilworth, Residuated lattices, Trans. Amer. Math. Soc.45 (1930), 335-354. MR1501995JFM65.0084.01

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