Lifting Modules Supplements and Projectivity in Module Theory
Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. There is a certain asymmetry in this duality. While the theory of extending modules is well documented in monographs and te
- PDF / 2,995,352 Bytes
- 403 Pages / 482.4 x 680.4 pts Page_size
- 79 Downloads / 214 Views
$GYLVRU\(GLWRULDO%RDUG /XLJL$PEURVLR 6FXROD1RUPDOH6XSHULRUH3LVD /HRQLG%XQLPRYLFK *HRUJLD,QVWLWXWHRI7HFKQRORJ\$WODQWD %HQRvW3HUWKDPH (FROH1RUPDOH6XSpULHXUH3DULV *HQQDG\6DPRURGQLWVN\ &RUQHOO8QLYHUVLW\5KRGHV+DOO ,JRU6KSDUOLQVNL 0DFTXDULH8QLYHUVLW\1HZ6RXWK:DOHV :ROIJDQJ6SU|VVLJ 78%HUJDNDGHPLH)UHLEHUJ
&- #LARK 4ITELEIINDD
%LUNKlXVHU9HUODJ %DVHO%RVWRQ%HUOLQ
&- #LARK 4ITELEIINDD
$XWKRUV -RKQ&ODUN 'HSDUWPHQWRI0DWKHPDWLFVDQG6WDWLVWLFV 8QLYHUVLW\RI2WDJR 32%R[ 'XQHGLQ 1HZ=HDODQG HPDLO MFODUN#PDWKVRWDJRDFQ]
1DUD\DQDVZDPL9DQDMD 'HSDUWPHQWRI0DWKHPDWLFV 8QLYHUVLW\RI0XPEDL 9LG\DQDJDUL0DUJ 0XPED\ ,QGLD HPDLO YDQDMDQDUD\DQDVZDPL#JPDLOFRP
&KULVWLDQ/RPS 'HSDUWDPHQWRGH0DWHPiWLFD3XUD )DFXOGDGHGH&LrQFLDV 8QLYHUVLGDGHGR3RUWR 5XD&DPSR$OHJUH 3RUWR 3RUWXJDO HPDLO FORPS#IFXSSW
5REHUW:LVEDXHU ,QVWLWXWHRI0DWKHPDWLFV +HLQULFK+HLQH8QLYHUVLW\'VVHOGRUI 8QLYHUVLWlWVVWU 'VVHOGRUI *HUPDQ\ HPDLO ZLVEDXHU#PDWKXQLGXHVVHOGRUIGH
0DWKHPDWLFDO6XEMHFW&ODVVL¿FDWLRQ''''' //3366
$&,3FDWDORJXHUHFRUGIRUWKLVERRNLVDYDLODEOHIURPWKH /LEUDU\RI&RQJUHVV:DVKLQJWRQ'&86$ %LEOLRJUDSKLFLQIRUPDWLRQSXEOLVKHGE\'LH'HXWVFKH%LEOLRWKHN 'LH'HXWVFKH%LEOLRWKHNOLVWVWKLVSXEOLFDWLRQLQWKH'HXWVFKH1DWLRQDOELEOLRJUD¿H GHWDLOHGELEOLRJUDSKLFGDWDLVDYDLODEOHLQWKH,QWHUQHWDW KWWS GQEGGEGH!
,6%1%LUNKlXVHU9HUODJ%DVHO±%RVWRQ±%HUOLQ 7KLVZRUNLVVXEMHFWWRFRS\ULJKW$OOULJKWVDUHUHVHUYHGZKHWKHUWKHZKROHRUSDUW RIWKHPDWHULDOLVFRQFHUQHGVSHFL¿FDOO\WKHULJKWVRIWUDQVODWLRQUHSULQWLQJUHXVH RILOOXVWUDWLRQVUHFLWDWLRQEURDGFDVWLQJUHSURGXFWLRQRQPLFUR¿OPVRULQRWKHUZD\V DQGVWRUDJHLQGDWDEDQNV)RUDQ\NLQGRIXVHSHUPLVVLRQRIWKHFRS\ULJKWRZQHU PXVWEHREWDLQHG %LUNKlXVHU9HUODJ32%R[&+%DVHO6ZLW]HUODQG 3DUWRI6SULQJHU6FLHQFH%XVLQHVV0HGLD &RYHUGHVLJQ %LUJLW%ORKPDQQ=ULFK6ZLW]HUODQG 3ULQWHGRQDFLGIUHHSDSHUSURGXFHGIURPFKORULQHIUHHSXOS7&)f 3ULQWHGLQ*HUPDQ\ ,6%1 H,6%1 ,6%1 ZZZELUNKDXVHUFK
&- #LARK 4ITELEIINDD
Contents Preface
vii
Introduction
ix
Notation
xiii
1 Basic notions 1 Preliminaries . . . . . . . . . . . . . . . . . 2 Small submodules and the radical . . . . . . 3 Cosmall inclusions and coclosed submodules 4 Projectivity conditions . . . . . . . . . . . . 5 Hollow dimension of modules . . . . . . . . 2 Preradicals and torsion theories 6 Preradicals and colocalisation . . . . . . . 7 Torsion theories . . . . . . . . . . . . . . . 8 Torsion theories related to small modules 9 Corational modules . . . . . . . . . . . . . 10 Proper
Data Loading...
