Forcing linearity numbers of certain types of infinitely generated modules over commutative rings /
Beyond the class of homomorphisms, there are other interesting classes of functions between modules. For example, consider the homogeneous functions M[](V) = { f : V [] V such that f(rv)=rf(v) for every r [] R and for every v [] V } where R is a commutative ring with identity and V is an R-module....
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
2001.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=728908681&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | Beyond the class of homomorphisms, there are other interesting classes of functions between modules. For example, consider the homogeneous functions M[](V) = { f : V [] V such that f(rv)=rf(v) for every r [] R and for every v [] V } where R is a commutative ring with identity and V is an R-module. The functions in M[](V) may or may not be linear in the sense that f(v+w) may not be equal to f(v)+f(w). Certain mathematicians have found a field of study in investigating how linear a class of functions is. One measure of their linearity is called the forcing linearity number. In this dissertation we determined the forcing linearity numbers for injective modules over Dedekind domains, semisimple modules over integral domains, and semicyclic modules over commutative Noetherian rings. |
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| Item Description: | Vita. "Major Subject: Mathematics". |
| Physical Description: | vi, 65 leaves ; 28 cm. Issued also on microfiche from University Microfilm Inc. |
| Bibliography: | Includes bibliographical references (leaves 63-64). |