The Torsion Submodule of A Cyclic Module Splits Off
1972 ◽
Vol 24
(3)
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pp. 450-464
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A prominent question in the study of modules over an integral domain has been: “When is the torsion submodule t(A) of a module A a direct summand of A?” A module is said to split when its torsion module is a direct summand. Clearly, every cyclic module over an integral domain splits. Interesting splitting problems have been explored by Kaplansky [14; 15], Rotman [20], Chase [4], and others.Recently, many concepts of torsion have been proposed for modules over arbitrary associative rings with identity. Two of the most important of these concepts are Goldie's torsion theory (see [1; 12; 22]) and the simple torsion theory (see [5; 6; 8; 9; 23], and their references).
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2015 ◽
Vol 22
(spec01)
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pp. 849-870
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1974 ◽
Vol 26
(6)
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pp. 1405-1411
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2004 ◽
Vol 70
(1)
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pp. 163-175
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1960 ◽
Vol 17
◽
pp. 147-158
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2011 ◽
Vol 18
(spec01)
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pp. 915-924
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