On commutative rings with uniserial dimension
2014 ◽
Vol 14
(01)
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pp. 1550008
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Keyword(s):
In this paper, we define and study a valuation dimension for commutative rings. The valuation dimension is a measure of how far a commutative ring deviates from being valuation. It is shown that a ring R with valuation dimension has finite uniform dimension. We prove that a ring R is Noetherian (respectively, Artinian) if and only if the ring R × R has (respectively, finite) valuation dimension if and only if R has (respectively, finite) valuation dimension and all cyclic uniserial modules are Noetherian (respectively, Artinian). We show that the class of all rings of finite valuation dimension strictly lies between the class of Artinian rings and the class of semi-perfect rings.
2012 ◽
Vol 11
(03)
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pp. 1250049
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Keyword(s):
2018 ◽
Vol 17
(07)
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pp. 1850125
Keyword(s):
1983 ◽
Vol 28
(1)
◽
pp. 9-12
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Keyword(s):
2019 ◽
Vol 18
(02)
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pp. 1950035
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2013 ◽
Vol 12
(04)
◽
pp. 1250199
◽
2011 ◽
Vol 10
(04)
◽
pp. 665-674
Keyword(s):
Keyword(s):