• Bulletin of the Korean Mathematical Society
• /
• v.42 no.3
• /
• pp.527-534
• /
• 2005

We consider countable rings with ascending chain condition on right annihilators. We determine the structure of a countable right p-injective Baer ring, a countable semi prime quasi-Baer ring and a countable quasi-Baer biregular ring.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.633-647
• /
• 2018

We compare the Lee and homogenous weights over the chain ring $S_{q,m}={\mathbb{F}}_q[u]/(u^m)$ by computing the minimum distance of random codes for small values of n, q, m.

• Journal of applied mathematics & informatics
• /
• v.38 no.1_2
• /
• pp.57-64
• /
• 2020

Let R ⊆ T be an ascending chain of commutative rings with identity and H(R, T) (resp., h(R, T)) the composite Hurwitz series ring (resp., composite Hurwitz polynomial ring). In this article, we give some conditions for the rings H(R, T) and h(R, T) to be PS-rings.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.6
• /
• pp.1713-1726
• /
• 2018

We study the one-sided regularity of matrices in upper triangular matrix rings in relation with the structure of diagonal entries. We next consider a ring theoretic condition that ab being regular implies ba being also regular for elements a, b in a given ring. Rings with such a condition are said to be commutative at regular product (simply, CRP rings). CRP rings are shown to be contained in the class of directly finite rings, and we prove that if R is a directly finite ring that satisfies the descending chain condition for principal right ideals or principal left ideals, then R is CRP. We obtain in particular that the upper triangular matrix rings over commutative rings are CRP.

• Journal of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1257-1268
• /
• 2018

In this article we first investigate a sort of unit-IFP ring by which Antoine provides very useful information to ring theory in relation with the structure of coefficients of zero-dividing polynomials. Here we are concerned with the whole shape of units and nilpotent elements in such rings. Next we study the properties of unit-IFP rings through group actions of units on nonzero nilpotent elements. We prove that if R is a unit-IFP ring such that there are finite number of orbits under the left (resp., right) action of units on nonzero nilpotent elements, then R satisfies the descending chain condition for nil left (resp., right) ideals of R and the upper nilradical of R is nilpotent.

• Kyungpook Mathematical Journal
• /
• v.18 no.1
• /
• pp.23-29
• /
• 1978

In [7) Scott has defined C-formation radical for a class C of near rings and has studied its porperties under chain conditions. A natural question that arises is: Does there exist a Lower C-Formation radical class L(M) containing a given class M of ideals of near rings in C? In this paper we answer this by giving. two constructions for L(M) and prove that prime radical is hereditary.

• East Asian mathematical journal
• /
• v.11 no.2
• /
• pp.153-167
• /
• 1995

• East Asian mathematical journal
• /
• v.36 no.3
• /
• pp.337-347
• /
• 2020

Let R be a ring with unity, and let I be an ideal of R. Then R is called I-semiregular if for every a ∈ R there exists b ∈ R such that ab is an idempotent of R and a - aba ∈ I. In this paper, basic properties of I-semiregularity are investigated, and some equivalent conditions to the primitivity of e are observed for an idempotent e of an I-semiregular ring R such that I∩eR = (0). For an abelian regular ring R with the ascending chain condition on annihilators of idempotents of R, it is shown that R is isomorphic to a direct product of a finite number of division rings, as a consequence of the observations.

• Journal of the Korean Mathematical Society
• /
• v.59 no.1
• /
• pp.193-204
• /
• 2022

We present construction methods for free self-orthogonal (self-dual or Type II) codes over ℤ₄[v]/〈v² + 2v〉 which is one of the finite commutative local non-chain Frobenius rings of order 16. By considering their Gray images on ℤ₄, we give a construct method for a code over ℤ₄. We have some new and optimal codes over ℤ₄ with respect to the minimum Lee weight or minimum Euclidean weight.

• Macromolecular Research
• /
• v.14 no.3
• /
• pp.306-311
• /
• 2006

New unsymmetrical ($\alpha$-Diimine)nickel(II) catalysts having different pendent groups at the ortho positions on aromatic rings were synthesized and subjected to propylene polymerizations with MAO (methylaluminoxane). Structural analyses of the resulting polypropylenes by $^1H\;and\;^{13}C\;NMR$ showed that the ortho substituents on aromatic rings of ($\alpha$-diimine)nickel(II) catalyst affected significantly the polypropylene microstructure. While $C_s$ symmetric catalyst afforded a syndiotactic polypropylene (rr triad content=66%) due to the syndiospecific chain end control, $C_1$ symmetric catalysts produced much less stereoregular polypropylenes (rr triads content <50%), presumably because of collision of the isospecific site control with the syndiospecific chain end control.