scholarly journals Square-free modules with the exchange property

2010 ◽  
Vol 323 (7) ◽  
pp. 1993-2001 ◽  
Author(s):  
Pace P. Nielsen
Keyword(s):  
Exchange Property ◽  
Free Modules

scholarly journals Relatively free algebras with weak exchange properties

2003 ◽  
Vol 75 (3) ◽  
pp. 355-384 ◽  
Author(s):  
John Fountain ◽  
Victoria Gould
Keyword(s):  
Principal Ideal ◽  
Exchange Property ◽  
Free Algebras ◽  
Weak Exchange ◽  
Free Modules ◽  
Principal Ideal Domains ◽  
Exchange Properties

AbstractWe consider algebras for which the operation PC of pure closure of subsets satisfies the exchange property. Subsets that are independent with respect to PC are directly independent. We investigate algebras in which PC satisfies the exchange property and which are relatively free on a directly independent generating subset. Examples of such algebras include independence algebras and dinitely generated free modules over principal ideal domains.

scholarly journals Commuting idempotents, square-free modules, and the exchange property

2015 ◽  
Vol 444 ◽  
pp. 52-80 ◽  
Author(s):  
Ryszard Mazurek ◽  
Pace P. Nielsen ◽  
Michał Ziembowski
Keyword(s):  
Exchange Property ◽  
Free Modules

scholarly journals Power graphs and exchange property for resolving sets

2019 ◽  
Vol 17 (1) ◽  
pp. 1303-1309 ◽  
Author(s):  
Ghulam Abbas ◽  
Usman Ali ◽  
Mobeen Munir ◽  
Syed Ahtsham Ul Haq Bokhary ◽  
Shin Min Kang
Keyword(s):  
Present Article ◽  
Linear Algebra ◽  
Finite Groups ◽  
Robot Navigation ◽  
Simple Graph ◽  
Exchange Property ◽  
Metric Dimension ◽  
Sufficient Condition ◽  
Resolving Set ◽  
Dihedral Groups

Abstract Classical applications of resolving sets and metric dimension can be observed in robot navigation, networking and pharmacy. In the present article, a formula for computing the metric dimension of a simple graph wihtout singleton twins is given. A sufficient condition for the graph to have the exchange property for resolving sets is found. Consequently, every minimal resolving set in the graph forms a basis for a matriod in the context of independence defined by Boutin [Determining sets, resolving set and the exchange property, Graphs Combin., 2009, 25, 789-806]. Also, a new way to define a matroid on finite ground is deduced. It is proved that the matroid is strongly base orderable and hence satisfies the conjecture of White [An unique exchange property for bases, Linear Algebra Appl., 1980, 31, 81-91]. As an application, it is shown that the power graphs of some finite groups can define a matroid. Moreover, we also compute the metric dimension of the power graphs of dihedral groups.

AB5*-modules with the exchange property

2021 ◽  
pp. 1-8
Author(s):  
Yasser Ibrahim ◽  
Mohamed Yousif
Keyword(s):  
Exchange Property

Ion-exchange property and mechanism of magnesium–calcium hydroxyapatite solid solutions

2004 ◽  
Vol 238 (1-3) ◽  
pp. 133-139 ◽  
Author(s):  
Akemi Yasukawa ◽  
Takashi Yokoyama ◽  
Kazuhiko Kandori ◽  
Tatsuo Ishikawa
Keyword(s):  
Ion Exchange ◽  
Solid Solutions ◽  
Calcium Hydroxyapatite ◽  
Exchange Property

Reaction Mechanisms of Li5La3Ta2O12 Powder with Ambient Air: H+/Li+ Exchange with Water

2012 ◽  
Vol 463-464 ◽  
pp. 123-127 ◽  
Author(s):  
Wei Guo Wang ◽  
Qian Feng Fang ◽  
Gang Ling Hao
Keyword(s):  
Internal Friction ◽  
Lithium Ion ◽  
Ambient Air ◽  
Exchange Property ◽  
Measured Temperature ◽  
Internal Friction Peak ◽  
Lower Temperature ◽  
Lithium Ion Conductors ◽  
Grain Surface ◽  
Water Gas

The proton/lithium exchange property of the garnet-related lithium-ion conductors Li5La3Ta2O12 is shown to occur at room temperature under ambient air. The internal friction, TGA analysis, and IR spectroscopy techniques are used to investigate the reaction mechanism. XRPD analysis demonstrates the topotactic character of the exchange reaction. The water gas in ambient air is adsorbed on the grain surface and then to exchange proton for lithium ion into the garnet structure,(Li5-xHx)La3Ta2O12. The H+/Li+ exchanging processes are reversible. When the measured temperature is higher over 573K, the internal friction peak gradually shifts toward lower temperature and the like garnet-like phase is recovered.

scholarly journals Almost free modules over modular group algebras

1976 ◽  
Vol 41 (2) ◽  
pp. 243-254 ◽  
Author(s):  
Jon F Carlson
Keyword(s):  
Modular Group ◽  
Group Algebras ◽  
Free Modules
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