Cartesian powers of the group of integers

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Title 
Cartesian powers of the group of integers 
Author 
Fink, Thorsten 
School 
Tulane University 
Academic Field 
Mathematics 
Abstract 
It is an important problem in group theory to determine whether or not direct summands of groups in a class belong again to the same class. The problem is particularly challenging for the class of cartesian powers $\doubz\sp\kappa$ of the group of integers $\doubz$ ($\kappa$ denotes a cardinal). In the absence of $\omega$measurable cardinals the problem is answered in the affirmative. But there are few results to date on direct sum decompositions of $\doubz\sp\kappa$ where $\kappa$ denotes an $\omega$measurable cardinal In this dissertation we construct examples of direct sum decompositions of cartesian powers $\doubz\sp\kappa$ = $\prod\sb{i\in\kappa}\langle e\sb{i}\rangle$ of the group of integers $\doubz$ where $\kappa$ denotes an $\omega$measurable cardinal, and $\langle e\sb{i}\rangle\cong\doubz$ for each $i\in\kappa$. The decompositions have the following form:$$\doubz\sp\kappa=A\oplus B,\ {\rm such\ that}\ e\sb{i}\in A\ {\rm for\ all}\ i\in\kappa$$ We introduce the notion of completely independent ultrafilters, and use that concept to derive sufficient conditions for a summand of $\doubz\sp\kappa$ to be isomorphic to $\doubz\sp\lambda$ for some cardinal $\lambda.$ Furthermore we show that summands of $R\sp\mu$, where $R<\doubq$ is a rational group and $\mu$ denotes the first measurable cardinal, are necessarily again powers of the rational group R 
Language 
eng 
Advisor(s) 
Fuchs, Laszlo 
Degree Date 
1996 
Degree 
Ph.D 
Publisher 
Tulane University 
Publication Date 
1996 
Source 
Source: 45 p., Dissertation Abstracts International, Volume: 5707, Section: B, page: 4434 
Identifier 
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Rights 
Copyright is in accordance with U.S. Copyright law 
Contact Information 
acase@tulane.edu 
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