Classes of commutative rings characterized by going-up and going-down behavior

David E. Dobbs; Marco Fontana

Rendiconti del Seminario Matematico della Università di Padova (1982)

  • Volume: 66, page 113-127
  • ISSN: 0041-8994

How to cite

top

Dobbs, David E., and Fontana, Marco. "Classes of commutative rings characterized by going-up and going-down behavior." Rendiconti del Seminario Matematico della Università di Padova 66 (1982): 113-127. <http://eudml.org/doc/107834>.

@article{Dobbs1982,
author = {Dobbs, David E., Fontana, Marco},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Baer ring; prime spectrum; going-down; going-up; Krull dimension zero; von Neumann regular rings; TYS-spaces; TF-spaces; pullback; pm-ring},
language = {eng},
pages = {113-127},
publisher = {Seminario Matematico of the University of Padua},
title = {Classes of commutative rings characterized by going-up and going-down behavior},
url = {http://eudml.org/doc/107834},
volume = {66},
year = {1982},
}

TY - JOUR
AU - Dobbs, David E.
AU - Fontana, Marco
TI - Classes of commutative rings characterized by going-up and going-down behavior
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1982
PB - Seminario Matematico of the University of Padua
VL - 66
SP - 113
EP - 127
LA - eng
KW - Baer ring; prime spectrum; going-down; going-up; Krull dimension zero; von Neumann regular rings; TYS-spaces; TF-spaces; pullback; pm-ring
UR - http://eudml.org/doc/107834
ER -

References

top
  1. [1] G. Artico - U. Marconi, On the compactness of minimal spectrum, Rend. Sem. Mat. Univ. Padova, 56 (1977), pp. 79-84. Zbl0381.13003MR480463
  2. [2] C.E. Aull - W.J. Thron, Separation axioms between T0 and T1, Indagat. Math., 24 (1962), pp. 26-37. Zbl0108.35402MR138082
  3. [3] M. Auslander, On regular group rings, Proc. Amer. Math. Soc., 8 (1957), pp. 658-664. Zbl0079.26703MR87670
  4. [4] N. Bourbaki, Algèbre Commutative, Chs. 1-2, Hermann, Paris, 1961. 
  5. [5] A. Conte, Proprietà di separazione della topologia di Zariski di uno schema, Rend. Ist. Lombardo Sc. A, 106 (1972), pp. 79-111. Zbl0254.14002MR349670
  6. [6] G. DeMARCO - A. ORSATTI, Commutative rings in which every prime ideal is contained in a unique maximal ideal, Proc. Amer. Math. Soc., 30 (1971), pp. 459-466. Zbl0207.05001MR282962
  7. [7] D.E. Dobbs - I. J. PAPICK, Going-down: a survey, Nieuw Arch. Wisk., 26 (1978), pp. 255-291. Zbl0383.13005MR491656
  8. [8] M. Fontana, Topologically defined classes of commutative rings, Annali Mat. Pura Appl., 123 (1980), pp. 331-355. Zbl0443.13001MR581935
  9. [9] M. Harada, Note on the dimension of modules and algebras, J. Inst. Polytech. Osaka City Univ.A, 7 (1956), pp. 17-27. Zbl0079.26702MR81269
  10. [10] B.W. Irlbeck, Finitely generated projective ideals in commutative rings, J. Reine Angew. Math., 298 (1978), pp. 98-100. Zbl0366.13003MR485829
  11. [11] I. Kaplansky, Commutative Rings, Allyn and Bacon, Boston, 1970. Zbl0203.34601MR254021
  12. [12] J.A. Kist, Minimal prime ideals in commutative semigroups, Proc. London Math. Soc., (3), 13 (1963), pp. 31-50. Zbl0108.04004MR143837
  13. [13] W.J. Lewis, The spectrum of a ring as a partially ordered set, J. Algebra, 25 (1973), pp. 419-434. Zbl0266.13010MR314811
  14. [14] W.J. Lewis - J. OHM, The ordering of Spec (R), Canad. J. Math., 28 (1976), pp. 820-835. Zbl0313.13003MR409428
  15. [15] T.P. Speed, A note on commutative Baer rings, J. Austral. Math. Soc., 14 (1972), pp. 257-263. Zbl0242.13003MR318120
  16. [16] W.V. Vasconcelos, Finiteness in projective ideals, J. Algebra, 25 (1973), pp. 269-278. Zbl0254.13012MR314828

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.