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Keywords
(1)
Valuation Ring
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Almost Maximal Valuation Rings
Almost Maximal Valuation Rings,10.1112/jlms/s24.1.140,Journal of The London Mathematical Societysecond Series,D. T. Gill
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Almost Maximal Valuation Rings
(
Citations: 26
)
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D. T. Gill
Journal:
Journal of The London Mathematical Societysecond Series  J LONDON MATH SOCSECOND SER
, vol. s24, no. 1, pp. 140146, 1971
DOI:
10.1112/jlms/s24.1.140
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jlms.oxfordjournals.org
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Citation Context
(9)
...Hence
M
is isomorphic to a submodule of
E
[
J
] which is uniserial by Gill (
1971
, Theorem)...
François Couchot
.
RDFlatness and RDInjectivity
...It is well known that finitely generated Rmodules need not be direct sums of cyclic modules unless R happens to be almost maximal (see Kaplansky [7], Gill [
6
])...
L. Fuchs
,
et al.
On modules over valuation domains whose finitely generated submodules ...
...(2) Over a local commutative ring R a module M is locally of serial type if and only if for every finitely generated module N in a[M] R/Ann (N) is an almost maximal valuation ring: Since R is commutative a[N] ~ R/Ann (N)Mod and the assertion follows from the theorem in Gill [
2
]...
R. Wisbauer
.
Modules locally of serial type
...KAP~,ANSXY [9], MATLIS [10] and GILL [
6
] showed that a valuation ring R is almost maximal if and only if every finitely generated Rmodule is a direct sum of cyclic modules...
Paolo Zanardo
.
Indecomposable finitely generated modules over valuation domains
...Only the third type presents any difficulty, and it is handled by techniques similar to those in [
G
]...
Thomas S. Shores
,
et al.
Decompositions of modules and matrices
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Citations
(26)
KERNELS OF MORPHISMS BETWEEN INDECOMPOSABLE INJECTIVE MODULES
(
Citations: 4
)
ALBERTO FACCHINI
,
ŞULE ECEVIT
,
M. TAMER KOŞAN
Journal:
Glasgow Mathematical Journal  GLASGOW MATH J
, vol. 52, no. A, pp. 6982, 2010
Flat modules over valuation rings
(
Citations: 3
)
Francois Couchot
Journal:
Journal of Pure and Applied Algebra  J PURE APPL ALG
, vol. 211, no. 1, pp. 235247, 2007
Pureinjective hulls of modules over valuation rings
(
Citations: 1
)
Francois Couchot
Journal:
Journal of Pure and Applied Algebra  J PURE APPL ALG
, vol. 207, no. 1, pp. 6376, 2006
RDFlatness and RDInjectivity
(
Citations: 1
)
François Couchot
Journal:
Communications in Algebra  COMMUN ALGEBRA
, vol. 34, no. 10, pp. 36753689, 2006
Injective modules and fpinjective modules over valuation rings
(
Citations: 4
)
Francois Couchot
Journal:
Journal of Algebra  J ALGEBRA
, vol. 267, no. 1, pp. 359376, 2003