• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.333-342
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• 2008

We introduce weak Armendariz ideals which are a generalization of ideals have the weakly insertion of factors property (or simply weakly IFP) and investigate their properties. Moreover, we prove that, if I is a weak Armendariz ideal of R, then I[x] is a weak Armendariz ideal of R[x]. As a consequence, we show that, R is weak Armendariz if and only if R[x] is a weak Armendariz ring. Also we obtain a generalization of [8] and [9].

• Korean Journal of Mathematics
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• v.26 no.3
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• pp.519-535
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• 2018

Let ${\mathcal{R}}$ denote the Galois ring of characteristic $p^n$, where p is a prime. In this paper, we investigate the elementary properties of Gauss sums over ${\mathcal{R}}$ in accordance with conditions of characters of Galois rings, and we restate results for Gauss sums in [1, 2, 3, 7, 12, 13]. Also, we compute the modulus of the Gauss sums.

• Korean Journal of Mathematics
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• v.26 no.3
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• pp.537-544
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• 2018

There is a standard construction of lifting cyclic codes over the prime finite field ${\mathbb{Z}}_p$ to the rings ${\mathbb{Z}}_{p^e}$ and to the ring of p-adic integers. We generalize this construction for arbitrary finite fields. This will naturally enable us to lift codes over finite fields ${\mathbb{F}}_{p^r}$ to codes over Galois rings GR($p^e$, r). We give concrete examples with all of the lifts.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1091-1097
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• 2009

In this paper, we investigate the extensions of generalized stable rings. It is shown that a ring R is a generalized stable ring if and only if R has a complete orthogonal set {e$_1$, . . . , e$_n$} of idempotents such that e$_1$Re$_1$, . . . , e$_n$Re$_n$ are generalized stable rings. Also, we prove that a ring R is a generalized stable ring if and only if R[[X]] is a generalized stable ring if and only if T(R,M) is a generalized stable ring.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.567-572
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• 2016

Quadratic residue codes are cyclic codes of prime length n defined over a finite field ${\mathbb{F}}_{p^e}$, where $p^e$ is a quadratic residue mod n. They comprise a very important family of codes. In this article we introduce the generalization of quadratic residue codes defined over Galois rings using the Galois theory.

• Journal of The Korean Astronomical Society
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• v.29 no.spc1
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• pp.45-48
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• 1996

Rings are common in disk galaxies. These rings are either indistinguishable from a pair of tightly wound spirals, or themselves are a part of the spiral structure. Furthermore, their occurrence is seen coincident with a bar in the center. In this paper, we interpret this spiral-ring structure as density waves resonantly excited by a rotating bar potential. The theory gives excellent agreement for the molecular spiral-rings in central parts. of nearby disk galaxies, observed by high resolution radio arrays. The same mechanism works for more distant spiral-rings in the outer parts of disk galaxies qualitatively, although the problem is complicated by the coupling of the stellar and gaseous disks.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.469-474
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• 2015

In this paper, we will consider the notions of (m, n)-potent conditions in near-rings, in particular, a near-ring R with left bipotent or right bipotent condition. We will derive some properties of near-rings with (1, n) and (n, 1)-potent conditions where n is a positive integer, and then some properties of near-rings with (m, n)-potent conditions. Also, we may discuss the behavior of R-subgroups in (1, n)-potent or (n, 1)-potent near-rings..

• East Asian mathematical journal
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• v.18 no.2
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• pp.245-259
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• 2002

In this paper, all rings or (left)near-rings R are associative, and for near-ring R, all R-groups are right R action and all modules are right R-modules. First, we begin with the study of rings in which all the additive endomorphisms or only the left multiplication endomorphisms are generated by ring endomorphisms and their properties. This study was motivated by the work on the Sullivan's Problem [14]. Next, for any right R-module M, we will introduce AM modules and investigate their basic properties. Finally, for any nearring R, we will also introduce MR-groups and study some of their properties.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.523-527
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• 2011

In this paper, We initiate a study of zero symmetric and constant parts of near-rings, and then apply these to self map near-rings. Next, we investigate that every near-ring can be embedded into some self map near-ring, and every zero symmetric near-ring can be embedded into some zero symmetric self map near-ring.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.1007-1010
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• 2011

In this paper, we begin with some basic concepts of substructures of near-rings, and then using some right substructures of near-rings, we may define the right semidirect sum of near-rings. Next, we investigate that every near-ring can be decomposed with right semidirect sum of right ideal by right R-subgroup, and then give some examples.