• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.527-534
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• 2005

We consider countable rings with ascending chain condition on right annihilators. We determine the structure of a countable right p-injective Baer ring, a countable semi prime quasi-Baer ring and a countable quasi-Baer biregular ring.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.645-658
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• 2008

In this paper, left-regular maps on d-algebras are defined. These mappings show behaviors reminiscent of homomorphisms on d-algebras which have been studied elsewhere. In particular for these mappings kernels, annihilators and co-annihilators are defined and some of their properties are investigated, especially in the setting of positive implicative d-algebras.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.521-541
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• 2017

In this note we elaborate first on well-known theorems for annihilators of polynomials over IFP rings by investigating the concrete shapes of nonzero constant annihilators. We consider next a generalization of IFP which preserves Abelian property, in relation with annihilators of polynomials, observing the basic structure of rings satisfying such condition.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.451-456
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• 2009

Let R be a ring. We give some new characterizations of QF under the special annihilators condition. Some known results are obtained as corollaries.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.333-341
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• 2005

A characterization of prime ideals is discussed. A relation between prime ideals and ideals of the form $A_w^{\wedge}$ is given. The prime ideal theorem is established. The notion of annihilators is introduced, and basic properties are investigated.

• East Asian mathematical journal
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• v.8 no.1
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• pp.63-67
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• 1992

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1267-1279
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• 2007

For a ring endomorphism ${\alpha}$ and an ${\alpha}-derivation\;{\delta}$ of a ring R, we study relation between the set of annihilators in R and the set of annihilators in nearring $R[x;{\alpha},{\delta}]\;and\;R_0[[x;{\alpha}]]$. Also we extend results of Armendariz on the Baer and p.p. conditions in a polynomial ring to certain analogous annihilator conditions in a nearring of skew polynomials. These results are somewhat surprising since, in contrast to the skew polynomial ring and skew power series case, the nearring of skew polynomials and skew power series have substitution for its "multiplication" operation.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.495-507
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• 2014

Nielsen and Rege-Chhawchharia called a ring R right McCoy if given nonzero polynomials f(x), g(x) over R with f(x)g(x) = 0, there exists a nonzero element r ${\in}$ R with f(x)r = 0. Hong et al. called a ring R strongly right McCoy if given nonzero polynomials f(x), g(x) over R with f(x)g(x) = 0, f(x)r = 0 for some nonzero r in the right ideal of R generated by the coefficients of g(x). Subsequently, Kim et al. observed similar conditions on linear polynomials by finding nonzero r's in various kinds of one-sided ideals generated by coefficients. But almost all results obtained by Kim et al. are concerned with the case of products of linear polynomials. In this paper we examine the nonzero annihilators in the products of general polynomials.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.359-365
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• 1995

Let R be a commutative ring with identity and M and R-module.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.345-349
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• 2010

Throughout this paper, we denote that R is a (right) near-ring and G an R-group. We will derive some properties of substructures and quotient substructures of Rand G.