• Korean Journal of Mathematics
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• 제18권1호
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• pp.97-103
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• 2010

It is well known that the group ring K[G] has the nontrivial Jacobson radical if K is a field of characteristic p and G is a finite group of which order is divided by a prime p. This paper is concerned with the structure of the Jacobson radical of such a group ring.

• 대한수학회보
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• 제45권4호
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• pp.757-762
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• 2008

In this paper, we generalize a few results of [7, 10] for lower radical classes of rings, by using the limit ordinal construction for lower radical classes of hemirings.

• Kyungpook Mathematical Journal
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• 제45권1호
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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.

• 충청수학회지
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• 제22권4호
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• pp.615-622
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• 2009

We solve the automatic continuity problem of an approximate higher derivation on a semisimple Banach algebra and investigate Hyers-Ulam stability for higher derivations.

• 호남수학학술지
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• 제29권2호
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• pp.289-297
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• 2007

In this paper, we show that BCI-algebras P and Q are injective if and only if its direct sum P $\oplus$ Q is injective. Moreover, we obtain the equivalent conditions for a p-semisimple BCI-algebra to be p-injective.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.273-278
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• 1997

Let A be a Banach algebra and B a semisimple annifilator Banach algebra. Then every homomorphism from A into B with range is continuous. Also we obtain condition s for the automatic continuity of homomorphism with dense range.

• 충청수학회지
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• 제12권1호
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• pp.33-41
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• 1999

In this paper, we introduce a new notion, called an QS-algebra, which is related to the areas of BCI/BCK-algebras and discuss the G-part of QS-algebras.

• 대한수학회보
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• 제33권4호
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• pp.531-536
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• 1996

Let $F$ denote $R$ or $C$. Put $A = SL(2, F)$. Define $P(F^2)$ to be the set of all 1-dimensional subspaces of $F^2$. Then the natural action of A on $F^2$ induces an action on $P(F^2)$.

• 대한수학회논문집
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• 제10권3호
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• pp.499-518
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• 1995

In this paper we consider more systematically the centralizer C(S) of the set $S = {f_a $\mid$ f_a : X \to X ; x \longmapsto x * a, a \in X}$ with respect to the semigroup End(X) of all endomorphisms of an implicative BCK-algebra X with the condition (S). We obtain a series of interesting results. The main results are stated as follows : (1) C(S) with repect to a binary operation * defined in a certain way forms a bounded implicative BCK-algebra with the condition (S). (2) X can be imbedded in C(S) such that X is an ideal of C(S)/ (3) If X is not bounded, it can be imbedded in a bounded subalgebra T of C(S) such that X is a maximal ideal of T. (4) If $X (\neq {0})$ is semisimple, C(S) is BCK-isomorphic to $\prod_{i \in I}{A_i}$ in which ${A_i}_{i \in I}$ is simple ideal family of X.

• 대한수학회보
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• 제54권2호
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• pp.559-571
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• 2017

We investigate modules M having the injective property relative to nonsingular modules. Such modules are called "$\mathcal{N}$-injective modules". It is shown that M is an $\mathcal{N}$-injective R-module if and only if the annihilator of $Z_2(R_R)$ in M is equal to the annihilator of $Z_2(R_R)$ in E(M). Every $\mathcal{N}$-injective R-module is injective precisely when R is a right nonsingular ring. We prove that the endomorphism ring of an $\mathcal{N}$-injective module has a von Neumann regular factor ring. Every (finitely generated, cyclic, free) R-module is $\mathcal{N}$-injective, if and only if $R^{(\mathbb{N})}$ is $\mathcal{N}$-injective, if and only if R is right t-semisimple. The $\mathcal{N}$-injective property is characterized for right extending rings, semilocal rings and rings of finite reduced rank. Using the $\mathcal{N}$-injective property, we determine the rings whose all nonsingular cyclic modules are injective.