• Kyungpook Mathematical Journal
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• 제51권1호
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• pp.1-10
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• 2011

Let (R, T) be a normal pair of commutative rings (i.e., R ${\subseteq}$ T is a unita extension of commutative rings, not necessarily integral domains, such that S is integrally closed in T for each ring S such that R ${\subseteq}$ S ${\subseteq}$ T) such that the total quotient ring of R is a von Neumann regular ring. Let P be one of the following ring-theoretic properties: going-down ring, extensionally going-down (EGD) ring, locally divided ring. Then R has P if and only if T has P. An example shows that the "if" part of the assertion fails if P is taken to be the "divided domain" property.

• 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.

• Kyungpook Mathematical Journal
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• 제46권4호
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• pp.597-601
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• 2006

We introduce in this paper the concept of idempotent reflexive right ideals and concern with rings containing an injective maximal right ideal. Some known results for reflexive rings and right HI-rings can be extended to idempotent reflexive rings. As applications, we are able to give a new characterization of regular right self-injective rings with nonzero socle and extend a known result for right weakly regular rings.

• 대한수학회보
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• 제57권1호
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• pp.207-218
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• 2020

Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group G with a maximal torus T is expressed as the ring of invariants, H*(BG; ℚ) ≅ H*(BT; ℚ)^W(G), which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod p reductions, we consider the structure of the rings, particularly for the Weyl group of symplectic groups Sp(n) and for the alternating groups A_n as the subgroup of W(SU(n)). We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod p cohomology of a space. For n = 3, 4, the rings under a conjugate of W(Sp(n)) are shown to be polynomial, and for n = 6, 8, they are non-polynomial. The structures of H*(BT^n-1; 𝔽_p)^A_n will be also discussed for n = 3, 4.

• 대한수학회보
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• 제45권3호
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• pp.457-466
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• 2008

Let R be a right near-ring. An R-group of type-5/2 which is a natural generalization of an irreducible (ring) module is introduced in near-rings. An R-group of type-5/2 is an R-group of type-2 and an R-group of type-3 is an R-group of type-5/2. Using it $J_{5/2}$, the Jacobson radical of type-5/2, is introduced in near-rings and it is observed that $J_2(R){\subseteq}J_{5/2}(R){\subseteq}J_3(R)$. It is shown that $J_{5/2}$ is an ideal-hereditary Kurosh-Amitsur radical (KA-radical) in the class of all zero-symmetric near-rings. But $J_{5/2}$ is not a KA-radical in the class of all near-rings. By introducing an R-group of type-(5/2)(0) it is shown that $J_{(5/2)(0)}$, the corresponding Jacobson radical of type-(5/2)(0), is a KA-radical in the class of all near-rings which extends the radical $J_{5/2}$ of zero-symmetric near-rings to the class of all near-rings.

• 대한수학회보
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• 제55권5호
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• pp.1371-1387
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• 2018

The classification of the self-dual codes over Galois rings GR(p, 2) and $GR(p^2,2)$ of length 4 is completed for all primes p up to equivalence in terms of automorphism group. We obtain all inequivalent classes and the number of each classes of self-dual codes for all primes.

• 충청수학회지
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• 제27권4호
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• pp.625-633
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• 2014

We study some results which concern the types of Noetherian local rings, and improve slightly the previous result: For a complete unmixed (or quasi-unmixed) Noetherian local ring A, we prove that if either $A_p$ is Cohen-Macaulay, or $r(Ap){\leq}depth$ $A_p+1$ for every prime ideal p in A, then A is Cohen-Macaulay. Also, some analogous results for modules are considered.

• Kyungpook Mathematical Journal
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• 제46권1호
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• pp.57-64
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• 2006

It is proved that if G is a direct sum of countable abelian $p$-groups and R is a special selected commutative unitary highly-generated ring of prime characteristic $p$, which ring is more general than the weakly perfect one, then the group of all normed units V (RG) modulo G, that is V (RG)=G, is a direct sum of countable groups as well. This strengthens a result due to W. May, published in (Proc. Amer. Math. Soc., 1979), that treats the same question but over a perfect ring.

• Kyungpook Mathematical Journal
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• 제32권2호
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• pp.219-228
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• 1992

• East Asian mathematical journal
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• 제3권
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• pp.55-60
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• 1987