scholarly journals A linear property of Goldie dimension of modules and modular lattices

2011 ◽  
Vol 215 (7) ◽  
pp. 1596-1605 ◽  
Author(s):  
Edmund R. Puczyłowski
Keyword(s):  
Modular Lattices ◽  
Goldie Dimension ◽  
Linear Property

scholarly journals GOLDIE DIMENSION, DUAL KRULL DIMENSION AND SUBDIRECT IRREDUCIBILITY

2010 ◽  
Vol 52 (A) ◽  
pp. 19-32 ◽  
Author(s):  
TOMA ALBU
Keyword(s):  
Krull Dimension ◽  
Subdirectly Irreducible ◽  
Modular Lattices ◽  
Survey Paper ◽  
Goldie Dimension ◽  
Subdirect Irreducibility ◽  
Upper Continuous ◽  
Torsion Theories ◽  
Quotient Modules ◽  
Noetherian Modules

AbstractIn this survey paper we present some results relating the Goldie dimension, dual Krull dimension and subdirect irreducibility in modules, torsion theories, Grothendieck categories and lattices. Our interest in studying this topic is rooted in a nice module theoretical result of Carl Faith [Commun. Algebra27 (1999), 1807–1810], characterizing Noetherian modules M by means of the finiteness of the Goldie dimension of all its quotient modules and the ACC on its subdirectly irreducible submodules. Thus, we extend his result in a dual Krull dimension setting and consider its dualization, not only in modules, but also in upper continuous modular lattices, with applications to torsion theories and Grothendieck categories.

scholarly journals On infinite Goldie dimension of modular lattices and modules

1985 ◽  
Vol 35 ◽  
pp. 151-155 ◽  
Author(s):  
P. Grzeszczuk ◽  
E.R. Puczyłowski
Keyword(s):  
Modular Lattices ◽  
Goldie Dimension

Goldie Dimension and Chain Conditions for Modular Lattices with Finite Group Actions

1986 ◽  
Vol 29 (3) ◽  
pp. 274-280 ◽  
Author(s):  
Piotr Grzeszczuk ◽  
Edmund R. Puczyłowski
Keyword(s):  
Finite Group ◽  
Fixed Points ◽  
Modular Lattice ◽  
Group Actions ◽  
Modular Lattices ◽  
Finite Group Actions ◽  
Chain Conditions ◽  
Goldie Dimension ◽  
A Finite Group

AbstractA relation between Goldie dimensions of a modular lattice L and its sublattice LG of fixed points under a finite group G of automorphisms of L is obtained. The method used also gives a relation between ACC (DCC) for L and for LG. The results obtained are applied to rings and modules.

scholarly journals LINEAR PROPERTIES OF GOLDIE DIMENSION OF MODULES AND MODULAR LATTICES

2010 ◽  
Vol 52 (A) ◽  
pp. 139-150 ◽  
Author(s):  
EDMUND R. PUCZYŁOWSKI
Keyword(s):  
Modular Lattices ◽  
Linear Spaces ◽  
Goldie Dimension

AbstractWe survey some old and recent results concerning the Goldie dimension of modules and modular lattices and its properties which are counterparts of properties of the dimension of linear spaces.

scholarly journals Seven-modular lattices and a septic base Jacobi identity

2003 ◽  
Vol 99 (2) ◽  
pp. 361-372 ◽  
Author(s):  
Heng Huat Chan ◽  
Kok Seng Chua ◽  
Patrick Solé
Keyword(s):  
Jacobi Identity ◽  
Modular Lattices

Matchings and Radon transforms in lattices II. Concordant sets

1987 ◽  
Vol 101 (2) ◽  
pp. 221-231 ◽  
Author(s):  
Joseph P. S. Kung
Keyword(s):  
Incidence Matrix ◽  
Finite Lattice ◽  
Möbius Function ◽  
Radon Transforms ◽  
Modular Lattices ◽  
Covering Theorem ◽  
Mobius Function ◽  
Finite Lattices ◽  
Semimodular Lattices

AbstractLet and ℳ be subsets of a finite lattice L. is said to be concordant with ℳ if, for every element x in L, either x is in ℳ or there exists an element x+ such that (CS1) the Möbius function μ(x, x+) ≠ 0 and (CS2) for every element j in , x ∨ j ≠ x+. We prove that if is concordant with ℳ, then the incidence matrix I(ℳ | ) has maximum possible rank ||, and hence there exists an injection σ: → ℳ such that σ(j) ≥ j for all j in . Using this, we derive several rank and covering inequalities in finite lattices. Among the results are generalizations of the Dowling-Wilson inequalities and Dilworth's covering theorem to semimodular lattices, and a refinement of Dilworth's covering theorem for modular lattices.

Improved Method Based on Fluid Mechanics Analysis for Buoy Gauge Design and Experimental Research

2012 ◽  
Vol 163 ◽  
pp. 133-137
Author(s):  
Ao Yu Chen ◽  
Xu Dong Pan ◽  
Guang Lin Wang
Keyword(s):  
Fluid Mechanics ◽  
Experimental Research ◽  
Traditional Method ◽  
New Method ◽  
Improved Method ◽  
Advanced Method ◽  
Inner Surface ◽  
Mechanics Analysis ◽  
Linear Property

Traditional method of buoy gauge design is rather complicated, so an advanced method by building and solving fluid mechanics equations is proposed in this paper. The curve of the taper pipe inner surface is calculated, according to different buoy gravity and diameter. In order to examine the effect of this improved method, an experiment is carried out. Results show that linear property of the buoy gauge improved by new method is excellent.

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