• Journal of Integrative Natural Science
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• v.10 no.4
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• pp.240-244
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• 2017

We study the behavior of some invariants under completion. We also give a counterexample, which is the same as a counterexample to Ding's Conjecture, to Koh-Lee's Conjecture.

• Kyungpook Mathematical Journal
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• v.45 no.1
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• pp.21-31
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• 2005

We introduce the notions of nilpotent element, quasi-regular element in a semiring which is a distributive lattice of rings. The concept of Jacobson radical is introduced for this kind of semirings.

• Honam Mathematical Journal
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• v.31 no.2
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• pp.203-217
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• 2009

In this note, we introduce a symmetric generalized 3-derivation in near-rings and investigate some conditions for a nearring to be a commutative ring.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.667-679
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• 2007

We study the prime ideal structure of the direct sum of directed system of rings indexed by a commutative semigroup which is nilpotent extension of a group.

• East Asian mathematical journal
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• v.36 no.1
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• pp.101-114
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• 2020

In this paper, we investigate commutativity of semiprime rings with a derivation which is strongly commutativity preserving and acts as a homomorphism or as an anti-homomorphism on a nonzero Lie ideal.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.261-264
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• 1994

Throughout this paper, all rings are assumed to be commutative with identity. By a local ring (R, m), we mean a Noetherian ring R which has the unique maximal ideal m. By dim(R) we always mean the Krull dimension of R. Let I be an ideal in a ring R and t an indeterminate over R. Then the Rees algebra R[It] is defined to be(omitted)

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.9-17
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• 2001

A ring R is called right mininjective if every isomorphsim between simple right ideals is given by left multiplication by an element of R. In this paper we consider that the necessary and sufficient condition for that Trivial extension of R by V, i.e. T(R; V ) is mininjective. We also study the split null extension R and S by V.

• Bulletin of the Korean Chemical Society
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• v.31 no.6
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• pp.1776-1778
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• 2010

• Journal of the Chungcheong Mathematical Society
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• v.16 no.2
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• pp.79-88
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• 2003

In this paper, we study properties of a free normalizing extension ring of a FI-extending ring. We develop properties of formal triangular matrix rings and FI-extending rings. Several results on the quasi-extending modules are obtained.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.153-167
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• 2006

We study permuting tri-derivations in ${\Gamma}$-rings and give an example.