• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.59-69
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• 2024

Let R be a commutative ring. An R-module E is said to be regular injective provided that Ext¹_R(R/I, E) = 0 for any regular ideal I of R. We first show that the class of regular injective modules have the hereditary property, and then introduce and study the regular injective dimension of modules and regular global dimension of rings. Finally, we give some homological characterizations of total rings of quotients and Dedekind rings.

• Kyungpook Mathematical Journal
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• v.26 no.2
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• pp.89-112
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• 1986

• The Mathematical Education
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• v.21 no.1
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• pp.45-46
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• 1982

• Journal for History of Mathematics
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• v.22 no.4
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• pp.115-128
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• 2009

In this paper, we modify the axiom of infinity of von Neumann's axioms modified by Pinter([5]), and then discuss an existence of an unknowable class in the system and a relationship between the unknowable class and the axiom of choice.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1207-1218
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• 2011

Let * be a star-operation on an integral domain R, and let $\mathfrak{I}_*^+(R)$ be the semigroup of *-invertible integral *-ideals of R. In this article, we introduce the concept of a *-coatom, and we then characterize when $\mathfrak{I}_*^+(R)$ is a free semigroup with a set of free generators consisting of *-coatoms. In particular, we show that $\mathfrak{I}_*^+(R)$ is a free semigroup if and only if R is a Krull domain and each ${\upsilon}$-invertible ${\upsilon}$-ideal is *-invertible. As a corollary, we obtain some characterizations of *-Dedekind domains.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1305-1320
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• 2018

We define new generalized factorials in several variables over an arbitrary subset ${\underline{S}}{\subseteq}R^n$, where R is a Dedekind domain and n is a positive integer. We then study the properties of the fixed divisor $d(\underline{S},f)$ of a multivariate polynomial $f{\in}R[x_1,x_2,{\ldots},x_n]$. We generalize the results of Polya, Bhargava, Gunji & McQuillan and strengthen that of Evrard, all of which relate the fixed divisor to generalized factorials of ${\underline{S}}$. We also express $d(\underline{S},f)$ in terms of the images $f({\underline{a}})$ of finitely many elements ${\underline{a}}{\in}R^n$, generalizing a result of Hensel, and in terms of the coefficients of f under explicit bases.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.797-811
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• 2024

In this paper, we define the torsion graph determined by equivalence classes of torsion elements and denote it by A_E(M). The vertex set of A_E(M) is the set of equivalence classes {[x] | x ∈ T(M)^*}, where two torsion elements x, y ∈ T(M)^* are equivalent if ann(x) = ann(y). Also, two distinct classes [x] and [y] are adjacent in A_E(M), provided that ann(x)ann(y)M = 0. We shall prove that for every torsion finitely generated module M over a Dedekind domain R, a vertex of A_E(M) has degree two if and only if it is an associated prime of M.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.711-715
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• 2012

In terms of divisible-like modules, some equivalent conditions for an integral domain R to be a generalized GCD domain are given.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.241-255
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• 2020

Let 𝔽_q be the finite field with q = p^m elements. A complex valued Cohn function defined on 𝔽_q is introduced in [1]. In this paper we define generalized Cohn functions on Galois rings and investigate their properties.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1007-1014
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• 2012

We derive the exact reciprocity formula connecting the twisted second moments at 1 for families of odd Dirichlet characters corresponding to two prime moduli, which parallels such formula discovered earlier for the special point 1/2.