• Journal of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.183-195
• /
• 2019

Let R be a commutative ring with unity. In this paper, we characterize the unit elements, the regular elements, the ${\pi}$-regular elements and the clean elements of zero-symmetric near-ring of polynomials $R_0[x]$, when $nil(R)^2=0$. Moreover, it is shown that the set of ${\pi}$-regular elements of $R_0[x]$ forms a semigroup. These results are somewhat surprising since, in contrast to the polynomial ring case, the near-ring of polynomials has substitution for its "multiplication" operation.

• Kyungpook Mathematical Journal
• /
• v.60 no.4
• /
• pp.839-851
• /
• 2020

We define morphic near-ring elements and study their behavior in regular near-rings. We show that the class of left morphic regular near-rings is properly contained between the classes of left strongly regular and unit-regular near-rings.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.401-409
• /
• 2000

In this paper, we determine the structure of ${\kappa}-potent$ elements and regular elements of the semigroup ${\Omega}_n$of doubly stochastic matrices of order n. In connection with this, we find the structure of the matrices X satisfying the equation AXA = A. From these, we determine a condition of a doubly stochastic matrix A whose Moore-Penrose generalized is also a doubly stochastic matrix.

• Journal of the Korean Mathematical Society
• /
• v.57 no.3
• /
• pp.793-807
• /
• 2020

Stable range of rings is a unifying concept for problems related to the substitution and cancellation of modules. The newly appeared element-wise setting for the simplest case of stable range one is tempting to study the lifting property modulo ideals. We study the lifting of elements having (idempotent) stable range one from a quotient of a ring R modulo a two-sided ideal I by providing several examples and investigating the relations with other lifting properties, including lifting idempotents, lifting units, and lifting of von Neumann regular elements. In the case where the ring R is a left or a right duo ring, we show that stable range one elements lift modulo every two-sided ideal if and only if R is a ring with stable range one. Under a mild assumption, we further prove that the lifting of elements having idempotent stable range one implies the lifting of von Neumann regular elements.

• Kyungpook Mathematical Journal
• /
• v.60 no.2
• /
• pp.307-318
• /
• 2020

This article concerns the class of rings which satisfy the property of inserting regular elements at zero products, and rings with such property are called regular-IFP. We study the structure of regular-IFP rings in relation to various ring properties that play roles in noncommutative ring theory. We investigate conditions under which the regular-IFPness pass to polynomial rings, and equivalent conditions to the regular-IFPness.

• Honam Mathematical Journal
• /
• v.42 no.1
• /
• pp.93-103
• /
• 2020

This article concerns a property of Abelain π-regular rings. A ring R shall be called right quasi-DR if for every a ∈ R there exists n ≥ 1 such that C(R)aⁿ ⊆ aR, where C(R) means the monoid of regular elements in R. The relations between the right quasi-DR property and near ring theoretic properties are investigated. We next show that the class of right quasi-DR rings is quite large.

• Communications of the Korean Mathematical Society
• /
• v.26 no.3
• /
• pp.373-384
• /
• 2011

In this paper we introduce and give some characterizations of (m, n)-regular le-${\Gamma}$-semigroup in terms of (m, n)-ideal elements and (m, n)-quasi-ideal elements. Also, we give some characterizations of subidempotent (m, n)-ideal elements in terms of $r_{\alpha}$- and $l_{\alpha}$- closed elements.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.5 no.6
• /
• pp.141-147
• /
• 1997

For the effective finite element analysis of the structures including material interfaces or contact surfaces, interface elements are proposed. Most of early works in this problem require not only iterative computation but also complex formulation because of the kinematic nonlinearities caused from the discontinuous behavior and the stress concentration phenomena. The proposed elements, however, are consistently formulated using relative displacements and tractions between top and bottom regular finite elements. The effectiveness of these elements are shown by solving various numerical sample problems including an leaf spring and comparing with results of general finite element analysis. As a result, more stable solutions are conveniently obtaines using interface elements than regular finite elements.

• Kyungpook Mathematical Journal
• /
• v.51 no.2
• /
• pp.139-143
• /
• 2011

In this paper we consider mappings ${\sigma}$ which map the binary operation symbol f to the term ${\sigma}$(f) which do not necessarily preserve the arities. We call these mappings generalized hypersubstitutions. Any generalized hypersubstitution ${\sigma}$ can be extended to a mapping $\hat{\sigma}$ on the set of all terms of type ${\tau}$ = (2). We de ne a binary operation on the set $Hyp_G$(2) of all generalized hypersubstitutions of type ${\tau}$ = (2) by using this extension The set $Hyp_G$(2) together with the identity generalized hypersubstitution ${\sigma}_{id}$ which maps f to the term f($x_1,x_2$) forms a monoid. We determine all regular elements of this monoid.

• The Journal of the Acoustical Society of Korea
• /
• v.18 no.1E
• /
• pp.20-26
• /
• 1999

Although the radiation impedance of a transducer with a regular square surface has been studied by many researchers, the formulas are still very complicated, which results in long computation time and low accuracy. In this paper, we propose a new algorithm for the calculation of acoustic radiation impedance in which the regular square vibrating surface of a transducer is divided into small elements and duplicate calculations are eliminated in the process of calculating mutual effects of the elements. Using this algorithm, shorter computation time and higher accuracy of results can be obtained. As a demonstration, the self and the mutual radiation impedance of transducers with a regular square surface are calculated and the accuracy of the results is evaluated.