Chain conditions in modular lattices

• Autorzy: M. Luísa Galvão , Patrick F. Smith
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1998
• Tom: 76
• Numer: 1
• Strony: 85-98

Daty

wydano

1998

otrzymano

1997-03-04

poprawiono

1997-07-02

Twórcy

autor

M. Luísa Galvão

• Departamento de Matemática, Universidade de Lisboa, 1699 Lisboa Codex, Portugal

autor

Patrick F. Smith

• Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, U.K.

Bibliografia

• [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.
• [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.
• [3] I. S. Alkhazzi, Modules, lattices and their direct summands, thesis, University of Glasgow 1992.
• [4] I. S. Alkhazzi and P. F. Smith, Modules with chain conditions on superfluous submodules, Comm. Algebra 19 (1991), 2331-2351.
• [5] F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer, 1992.
• [6] K. R. Goodearl, Singular Torsion and the Splitting Properties, Mem. Amer. Math. Soc. 124 (1972).
• [7] P. Grzeszczuk, The Goldie dimension of some extensions of modular lattices, in: Contemp. Math. 131, Part 3, Amer. Math. Soc., 1992, 111-119.
• [8] P. Grzeszczuk and E. R. Puczyłowski, On Goldie and dual Goldie dimensions, J. Pure Appl. Algebra 31 (1984), 47-54.
• [9] B. Lemonnier, Déviation des ensembles et groupes abéliens totalement ordonnés, Bull. Sci. Math. 96 (1972), 289-303.
• [10] C. Năstăsescu and F. van Oystaeyen, Dimensions of Ring Theory, Reidel, 1987.
• [11] E. R. Puczyłowski, On finiteness conditions of modular lattices, preprint.
• [12] P. F. Smith, Modules with many direct summands, Osaka J. Math. 27 (1990), 253-264.
• [13] O. Zariski and P. Samuel, Commutative Algebra, Vol. I, Van Nostrand, 1958.