On the Krull-Schmidt theorem for Artinian modules

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On the Krull-Schmidt theorem for Artinian modules. / Pimenov, K. I.

In: Journal of Mathematical Sciences, Vol. 110, No. 6, 01.01.2002, p. 3140-3142.

Research output: Contribution to journal › Article › peer-review

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Pimenov, K. I. / On the Krull-Schmidt theorem for Artinian modules. In: Journal of Mathematical Sciences. 2002 ; Vol. 110, No. 6. pp. 3140-3142.

BibTeX

@article{808b6453ab4e46ada084c74158bd666d,

title = "On the Krull-Schmidt theorem for Artinian modules",

abstract = "A property of rings generalizing commutativity is introduced. If a ring satisfies this property, then the Krull-Schmidt theorem holds for Artinian modules over the ring. In particular, this property is fulfilled for local rings of finite rank and for rings such that their centers are surjectively mapped by the natural projection onto the factor with respect to the radical of the ring. A local ring for which the property fails is constructed; for the direct decompositions of Artinian modules over this ring there appear anomalies similar to the anomalies of direct decompositions of torsion-free Abelian groups of finite rank.",

author = "Pimenov, {K. I.}",

year = "2002",

month = jan,

day = "1",

doi = "10.1023/A:1015428513193",

language = "English",

volume = "110",

pages = "3140--3142",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "6",

}

RIS

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T1 - On the Krull-Schmidt theorem for Artinian modules

AU - Pimenov, K. I.

PY - 2002/1/1

Y1 - 2002/1/1

N2 - A property of rings generalizing commutativity is introduced. If a ring satisfies this property, then the Krull-Schmidt theorem holds for Artinian modules over the ring. In particular, this property is fulfilled for local rings of finite rank and for rings such that their centers are surjectively mapped by the natural projection onto the factor with respect to the radical of the ring. A local ring for which the property fails is constructed; for the direct decompositions of Artinian modules over this ring there appear anomalies similar to the anomalies of direct decompositions of torsion-free Abelian groups of finite rank.

AB - A property of rings generalizing commutativity is introduced. If a ring satisfies this property, then the Krull-Schmidt theorem holds for Artinian modules over the ring. In particular, this property is fulfilled for local rings of finite rank and for rings such that their centers are surjectively mapped by the natural projection onto the factor with respect to the radical of the ring. A local ring for which the property fails is constructed; for the direct decompositions of Artinian modules over this ring there appear anomalies similar to the anomalies of direct decompositions of torsion-free Abelian groups of finite rank.

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U2 - 10.1023/A:1015428513193

DO - 10.1023/A:1015428513193

M3 - Article

AN - SCOPUS:52649104534

VL - 110

SP - 3140

EP - 3142

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -

ID: 36910594