• Honam Mathematical Journal
• /
• v.34 no.4
• /
• pp.571-584
• /
• 2012

In this study, we investigate the concept of zero-divisor graphs of multiplication modules over commutative rings as a natural generalization of zero-divisor graphs of commutative rings. In particular, we study the zero-divisor graphs of the module $\mathbb{Z}_n$ over the ring $\mathbb{Z}$ of integers, where $n$ is a positive integer greater than 1.

• Communications of the Korean Mathematical Society
• /
• v.23 no.4
• /
• pp.499-509
• /
• 2008

In [4] we showed that a polynomial over a Noetherian ring is divisible by some other polynomial by looking at the matrix formed by the coefficients of the polynomials which we called the resultant matrix. Using the result, we will find conditions for a polynomial over a commutative ring to be irreducible. This can be viewed as a generalization of the Eisenstein's irreducibility criterion.

• Korean Journal of Mathematics
• /
• v.18 no.3
• /
• pp.271-275
• /
• 2010

Let R be a commutative ring with identity, T(R) be the total quotient ring of R, and D be a ring such that $R{\subseteq}D{\subseteq}T(R)$ and D is a finite R-module. In this paper, we show that each regular ideal of R is finitely generated if and only if each regular ideal of D is finitely generated. This is a generalization of the Eakin-Nagata theorem that R is Noetherian if and only if D is Noetherian.

• Journal of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.271-281
• /
• 2006

The commutative products of the distributions $x^r\;ln^p\;{\mid}x{\mid}\;and\;x^{-r-1}ln^q\;{\mid}x{\mid}$ and of sgn x $x^r\;ln^p\;{\mid}x{\mid}\;and\;sgn\;x\;x^{-r-1}ln^q\;{\mid}x{\mid}$ are evaluated for $r=0,\;\pm1,\;\pm2,...\;and\;p,\;q=0,1,2,....$

• Communications of the Korean Mathematical Society
• /
• v.31 no.2
• /
• pp.209-216
• /
• 2016

In this paper, we introduce the notion of symmetric bi-derivations of a B-algebra and investigate some related properties. We study the notion of symmetric bi-derivations of a 0-commutative B-algebra and state some related properties.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.371-381
• /
• 2020

A ring R is called right pure-injective if it is injective with respect to pure exact sequences. According to a well known result of L. Melkersson, every commutative Artinian ring is pure-injective, but the converse is not true, even if R is a commutative Noetherian local ring. In this paper, a series of conditions under which right pure-injective rings are either right Artinian rings or quasi-Frobenius rings are given. Also, some of our results extend previously known results for quasi-Frobenius rings.

• Communications of the Korean Mathematical Society
• /
• v.19 no.3
• /
• pp.427-433
• /
• 2004

Conditions for a $\Gamma$-near-ring to be commutative are investigated.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.5
• /
• pp.1077-1087
• /
• 2010

Anderson-Smith [1] studied weakly prime ideals for a commutative ring with identity. Blair-Tsutsui [2] studied the structure of a ring in which every ideal is prime. In this paper we investigate the structure of rings, not necessarily commutative, in which all ideals are weakly prime.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.31-35
• /
• 2020

With the motivation to extend the Zelasko's theorem on commutative algebras, it was shown in [2] that if n ∈ {3, 4} is fixed, A, B are commutative algebras and h : A → B is an n-Jordan homomorphism, then h is an n-ring homomorphism. In this paper, we extend this result for all n ≥ 3.

• Korean Journal of Mathematics
• /
• v.12 no.1
• /
• pp.23-32
• /
• 2004

Let (B, $m_B$, ${\kappa}$) be a maximal commutative ${\kappa}$-subalgebra of a matrix algebra $M_n(\kappa)$. We will construct a maximal commutative ${\kappa}$-subalgebra (R, $m$, ${\kappa}$) of $M_n+3(\kappa)$ from the algebra B such that the algebra R has dimension greater than the dimension of B by 3. Moreover, we will show a $C_i$-construction doesn't imply a $C^3_2$-construction for $i=1,2$.