• Communications of the Korean Mathematical Society
• /
• v.29 no.3
• /
• pp.463-478
• /
• 2014

We find criteria for symmetrized monomials to be non-hit in the $\mathcal{A}_2$-algebra of symmetric polynomials in three variables, where $\mathcal{A}_2$ is the mod 2 Steenrod algebra.

• Korean Journal of Mathematics
• /
• v.6 no.2
• /
• pp.137-148
• /
• 1998

We briefly discuss the Lie groups, it's nilpotency and representations of a nilpotent Lie groups. Dixmier and Kirillov proved that simply connected nilpotent Lie groups over $\mathbb{R}$ are monomial. We reformulate the above result at the Lie algebra level.

• Journal of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.543-555
• /
• 2013

We consider powers of lexsegment ideals with a linear resolution (equivalently, with linear quotients) which are not completely lexsegment ideals. We give a complete description of their minimal graded free resolution.

• Communications of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.85-101
• /
• 2018

Let S be a polynomial ring over a field K, with a monomial order ${\prec}$, and let I be an unmixed graded ideal of S. In this paper we study two functions associated to I: The minimum distance function ${\delta}_I$ and the footprint function $fp_I$. It is shown that ${\delta}_I$ is positive and that $fp_I$ is positive if the initial ideal of I is unmixed. Then we show that if I is radical and its associated primes are generated by linear forms, then ${\delta}_I$ is strictly decreasing until it reaches the asymptotic value 1. If I is the edge ideal of a Cohen-Macaulay bipartite graph, we show that ${\delta}_I(d)=1$ for d greater than or equal to the regularity of S/I. For a graded ideal of dimension ${\geq}1$, whose initial ideal is a complete intersection, we give an exact sharp lower bound for the corresponding minimum distance function.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.4
• /
• pp.1353-1363
• /
• 2015

Let D be a division ring and w($x_1,\;x_2,\;{\ldots},\;x_m$) be a generalized group monomial over $D^*$. In this paper, we investigate subnormal subgroups and maximal subgroups of $D^*$ which satisfy the identity $w(x_1,\;x_2,\;{\ldots},\;x_m)=1$.

• Journal of the Korean Mathematical Society
• /
• v.40 no.6
• /
• pp.943-950
• /
• 2003

The maximal column rank of an m by n matrix A over max algebra is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over max algebra. We also characterize the linear operators which preserve the maximal column rank of matrices over max algebra.

• Journal of the Korean Mathematical Society
• /
• v.46 no.3
• /
• pp.621-642
• /
• 2009

In this paper we give necessary and sufficient conditions that two Toeplitz operators with monomial symbols acting on the weighted Bergman space commute. We also present necessary and sufficient conditions for the hyponormality of Toeplitz operators with some special symbols on the weighted Bergman space. All the results are stated in terms of the Mellin transform of the symbol.

• Journal of the Chungcheong Mathematical Society
• /
• v.7 no.1
• /
• pp.153-164
• /
• 1994

Let A be a commutative ring with identity and M an A-module. When $U_n$ is a triangular subset of $A_n$, Sharp and Zakeri defined a module of generalized fractions $U_n^{-n}M$. In [SZ3], they described a relation of the Monomial Conjecture and a module of generalized fractions under the condition of a Noetherian local ring. In this paper, we investigate some properties of non-zero generalized fractions and give a generalization of results of Sharp and Zakeri for an arbitrary ring.

• Journal of the Chungcheong Mathematical Society
• /
• v.31 no.1
• /
• pp.103-130
• /
• 2018

In the paper we establish some new results depending on the comparative growth properties of composite entire and meromorphic functions using relative $_pL^*-order$, relative $_pL^*-lower$ order and differential monomials, differential polynomials generated by one of the factors.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.269-275
• /
• 2021

Let ℝ be the set of real numbers, f, g : ℝ → ℝ and �� ≥ 0. In this paper, we consider the stability of partially pexiderized exponential-radical functional equation $$f({\sqrt[n]{x^N+y^N}})=f(x)g(y)$$ for all x, y ∈ ℝ, i.e., we investigate the functional inequality $$\|f({\sqrt[n]{x^N+y^N}})-f(x)g(y)\|{\leq}{\epsilon}$$ for all x, y ∈ ℝ.