• 대한수학회보
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• 제55권2호
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• pp.675-677
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• 2018

• 대한수학회보
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• 제50권6호
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• pp.1855-1861
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• 2013

Let R be a commutative Noetherian ring, I an ideal of R, M and N two R-modules. We characterize the least integer i such that $H^i_I(M,N)$ is not weakly Artinian by using the notion of weakly filter regular sequences. Also, a local-global principle for minimax generalized local cohomology modules is shown and the result generalizes the corresponding result for local cohomology modules.

• 대한수학회보
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• 제47권4호
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• pp.715-726
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• 2010

We continue the study of fully idempotent rings initiated by Courter. It is shown that a (semi)prime ring, but not fully idempotent, can be always constructed from any (semi)prime ring. It is shown that the full idempotence is both Morita invariant and a hereditary radical property, obtaining $hs(Mat_n(R))\;=\;Mat_n(hs(R))$ for any ring R where hs(-) means the sum of all fully idempotent ideals. A non-semiprimitive fully idempotent ring with identity is constructed from the Smoktunowicz's simple nil ring. It is proved that the full idempotence is preserved by the classical quotient rings. More properties of fully idempotent rings are examined and necessary examples are found or constructed in the process.

• 대한수학회보
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• 제57권4호
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• pp.945-956
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• 2020

We introduce the concept of S-exchange rings to unify various subclass of exchange rings, where S is a subset of the ring. Many properties on S-exchange rings are obtained. For instance, we show that a ring R is clean if and only if R is left U(R)-exchange, a ring R is nil clean if and only if R is left (N(R) - 1)-exchange, and that a ring R is J-clean if and only if R is left (J(R) - 1)-exchange. As a conclusion, we obtain a sufficient condition such that clean (nil clean property, respectively) can pass to corners and reprove that J-clean passes to corners by a different way.

• 호남수학학술지
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• 제38권2호
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• pp.259-267
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• 2016

A module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. Recently, the authors introduced the classes of QTAG-modules namely as socle-regular and strongly socle-regular QTAG-modules which properly contain the classes of transitive and fully transitive QTAG-modules respectively. Here we define strongly and quasi transitivities and study the inter relations between various type of transitivities.