Chain conditions in modular lattices

M. Galvão; Patrick Smith

Colloquium Mathematicae (1998)

  • Volume: 76, Issue: 1, page 85-98
  • ISSN: 0010-1354

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Galvão, M., and Smith, Patrick. "Chain conditions in modular lattices." Colloquium Mathematicae 76.1 (1998): 85-98. <http://eudml.org/doc/210554>.

@article{Galvão1998,
author = {Galvão, M., Smith, Patrick},
journal = {Colloquium Mathematicae},
keywords = {chain conditions; modular lattice; essential elements; Noetherian; Krull dimension; finite Goldie dimension; semi-essential element},
language = {eng},
number = {1},
pages = {85-98},
title = {Chain conditions in modular lattices},
url = {http://eudml.org/doc/210554},
volume = {76},
year = {1998},
}

TY - JOUR
AU - Galvão, M.
AU - Smith, Patrick
TI - Chain conditions in modular lattices
JO - Colloquium Mathematicae
PY - 1998
VL - 76
IS - 1
SP - 85
EP - 98
LA - eng
KW - chain conditions; modular lattice; essential elements; Noetherian; Krull dimension; finite Goldie dimension; semi-essential element
UR - http://eudml.org/doc/210554
ER -

References

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  1. [1] T. Albu and P. F. Smith, Localization of modular lattices, Krull dimension, and the Hopkins-Levitzki theorem (I), Math. Proc. Cambridge Philos. Soc. 120 (1996), 87-101. Zbl0854.06008
  2. [2] T. Albu and P. F. Smith, Localization of modular lattices, Krull dimension, and the Hopkins-Levitzki theorem (II), Comm. Algebra 25 (1997), 1111-1128. Zbl0878.06006
  3. [3] I. S. Alkhazzi, Modules, lattices and their direct summands, thesis, University of Glasgow 1992. 
  4. [4] I. S. Alkhazzi and P. F. Smith, Modules with chain conditions on superfluous submodules, Comm. Algebra 19 (1991), 2331-2351. Zbl0734.16009
  5. [5] F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer, 1992. Zbl0765.16001
  6. [6] K. R. Goodearl, Singular Torsion and the Splitting Properties, Mem. Amer. Math. Soc. 124 (1972). 
  7. [7] P. Grzeszczuk, The Goldie dimension of some extensions of modular lattices, in: Contemp. Math. 131, Part 3, Amer. Math. Soc., 1992, 111-119. Zbl0771.16014
  8. [8] P. Grzeszczuk and E. R. Puczyłowski, On Goldie and dual Goldie dimensions, J. Pure Appl. Algebra 31 (1984), 47-54. Zbl0528.16010
  9. [9] B. Lemonnier, Déviation des ensembles et groupes abéliens totalement ordonnés, Bull. Sci. Math. 96 (1972), 289-303. Zbl0258.06002
  10. [10] C. Năstăsescu and F. van Oystaeyen, Dimensions of Ring Theory, Reidel, 1987. 
  11. [11] E. R. Puczyłowski, On finiteness conditions of modular lattices, preprint. Zbl0914.06003
  12. [12] P. F. Smith, Modules with many direct summands, Osaka J. Math. 27 (1990), 253-264. Zbl0703.16007
  13. [13] O. Zariski and P. Samuel, Commutative Algebra, Vol. I, Van Nostrand, 1958. Zbl0081.26501

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