• Communications of the Korean Mathematical Society
• /
• v.18 no.2
• /
• pp.215-223
• /
• 2003

Parks [7] showed that there is an one to one correspondence between good pairs of subgroups in G and irreducible monomial characters of G. This provides a useful criterion for a group to be monomial. In this paper, we study relative monomial groups by defining triples in G, and find relationships between the triples and irreducible relative monomial characters.

• Communications of the Korean Mathematical Society
• /
• v.11 no.3
• /
• pp.627-631
• /
• 1996

We prove that some monomial curves are set-theoretic complete intersection of two surfaces. We also give explicity the equations of corresponding surfaces.

• Bulletin of the Korean Mathematical Society
• /
• v.45 no.2
• /
• pp.397-403
• /
• 2008

In this paper, we modify L. $C\breve{a}dariu$ and V. Radu's result for the stability of the monomial functional equation $\sum\limits_{n=0}^{n}n\;C_i(-1)^{n-i}f(ix+y)-n!f(x)=0$ in the sense of Th. M. Rassias. Also, we investigate the superstability of the monomial functional equation.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.239-246
• /
• 1999

We extend the Ding's vanishing theorem of $\delta$-invariant slightly on a Cohen-Macaulay local ring using the concept of Golod paris. we also investigate the relation between the vanishing of $\delta$-invariant and Hochster's Monomial Conjecture.

• Communications of the Korean Mathematical Society
• /
• v.15 no.3
• /
• pp.481-492
• /
• 2000

As an application of Clifford theory, we are interested in a situation in which every irreducible projective character of a finite group G is an induced character of an irreducible linear character of some subgroup H of G. For this purpose, we study relative projective monomial groups with respect to subgroups.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.711-720
• /
• 2021

Let R denote a commutative noetherian ring, and let 𝐱 := x1, …, xd be an R-regular sequence. Suppose that 𝖆 denotes a monomial ideal with respect to 𝐱. The first purpose of this article is to show that 𝖆 is irreducible if and only if 𝖆 is a generalized-parametric ideal. Next, it is shown that, for any integer n ≥ 1, (x1, …, xd)n = ⋂P(f), where the intersection (irredundant) is taken over all monomials f = xe11 ⋯ xedd such that deg(f) = n - 1 and P(f) := (xe1+11, ⋯, xed+1d). The second main result of this paper shows that if 𝖖 := (𝐱) is a prime ideal of R which is contained in the Jacobson radical of R and R is 𝖖-adically complete, then 𝖆 is a parameter ideal if and only if 𝖆 is a monomial irreducible ideal and Rad(𝖆) = 𝖖. In addition, if a is generated by monomials m1, …, mr, then Rad(𝖆), the radical of a, is also monomial and Rad(𝖆) = (ω1, …, ωr), where ωi = rad(mi) for all i = 1, …, r.

• Journal of the Korean Mathematical Society
• /
• v.37 no.1
• /
• pp.55-72
• /
• 2000

In this paper, we develop the Grobner-Shirshov basis theory for the representations of associative algebras by introducing the notion of Grobner-Shirshov pairs. Our result can be applied to solve the reduction problem in representation theory and to construct monomial bases of representations of associative algebras. As an illustration, we give an explicit construction of Grobner-Shirshov pairs and monomial bases for finite dimensional irreducible representations of the simple tie algebra sl$_3$. Each of these monomial bases is in 1-1 correspondence with the set of semistandard Young tableaux with a given shape.

• Journal of the Korean Mathematical Society
• /
• v.45 no.3
• /
• pp.711-725
• /
• 2008

We give an explicit construction of Grobner-Shirshov pairs and monomial bases for finite-dimensional irreducible representations of the simple Lie algebra $sp_4$. We also identify the monomial basis consisting of the reduced monomials with a set of semistandard tableaux of a given shape, on which we give a colored oriented graph structure.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.147-160
• /
• 2024

In this paper, we define two new classes of monomial ideals I_𝑙,d and J_k,d. When d ≥ 2k + 1 and 𝑙 ≤ d - k - 1, we give the exact formulas to compute the depth and Stanley depth of quotient rings S/I^t_𝑙,d for all t ≥ 1. When d = 2k = 2𝑙, we compute the depth and Stanley depth of quotient ring S/I_𝑙,d. When d ≥ 2k, we also compute the depth and Stanley depth of quotient ring S/J_k,d.

• Journal of applied mathematics & informatics
• /
• v.37 no.3_4
• /
• pp.281-294
• /
• 2019

In this paper, we study the results concerning uniqueness of meromorphic functions sharing a small function and present one theorem which extend and improves previous results.