BOUNDED AND FULLY BOUNDED MODULES
2011 ◽
Vol 84
(3)
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pp. 433-440
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AbstractGeneralizing the concept of right bounded rings, a module MR is called bounded if annR(M/N)≤eRR for all N≤eMR. The module MR is called fully bounded if (M/P) is bounded as a module over R/annR(M/P) for any ℒ2-prime submodule P◃MR. Boundedness and right boundedness are Morita invariant properties. Rings with all modules (fully) bounded are characterized, and it is proved that a ring R is right Artinian if and only if RR has Krull dimension, all R-modules are fully bounded and ideals of R are finitely generated as right ideals. For certain fully bounded ℒ2-Noetherian modules MR, it is shown that the Krull dimension of MR is at most equal to the classical Krull dimension of R when both dimensions exist.
2017 ◽
Vol 37
(1)
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pp. 153-168
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2014 ◽
Vol 13
(06)
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pp. 1450015
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2010 ◽
Vol 52
(A)
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pp. 19-32
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2010 ◽
Vol 09
(01)
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pp. 73-122
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1973 ◽
Vol 3
(4)
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pp. 385-397
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1977 ◽
Vol 29
(4)
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pp. 874-888
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1978 ◽
Vol 21
(3)
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pp. 373-375
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