• Kyungpook Mathematical Journal
• /
• v.61 no.3
• /
• pp.461-472
• /
• 2021

We study a new ring property called axis-commutativity. Axis-commutative rings are seated between commutative rings and duo rings and are a generalization of division rings. We investigate the basic structure and several extensions of axis-commutative rings.

• Journal of Integrative Natural Science
• /
• v.8 no.4
• /
• pp.313-316
• /
• 2015

In this article, we compute the order of a general linear group $GL_n(A)$ over a finite ring A.

• Journal of the Korean Mathematical Society
• /
• v.53 no.3
• /
• pp.519-532
• /
• 2016

The zero-divisor graph of a noncommutative ring R, denoted by ${\Gamma}(R)$, is a graph whose vertices are nonzero zero-divisors of R, and there is a directed edge from a vertex x to a distinct vertex y if and only if xy = 0. Let $R=M_2(F_q)$ be the $2{\times}2$ matrix ring over a finite field $F_q$. In this article, we investigate the automorphism group of ${\Gamma}(R)$.

• Journal of the Korean Mathematical Society
• /
• v.47 no.2
• /
• pp.247-261
• /
• 2010

An associative ring R with identity is called a clean ring if every element of R is the sum of a unit and an idempotent. In this paper, we introduce the concept of f-clean rings. We study various properties of f-clean rings. Let C = $\(\array{A\;V\\W\;B}\)$ be a Morita Context ring. We determine conditions under which the ring C is f-clean. Moreover, we introduce the concept of rings having many full elements. We investigate characterizations of this kind of rings and show that rings having many full elements are closed under matrix rings and Morita Context rings.

• Kyungpook Mathematical Journal
• /
• v.58 no.2
• /
• pp.203-219
• /
• 2018

This paper is devoted to the study of strongly ${\alpha}-semicommutative$ rings, a generalization of strongly semicommutative and ${\alpha}-rigid$ rings. Although the n-by-n upper triangular matrix ring over any ring with identity is not strongly ${\bar{\alpha}}-semicommutative$ for $n{\geq}2$, we show that a special subring of the upper triangular matrix ring over a reduced ring is strongly ${\bar{\alpha}}-semicommutative$ under some additional conditions. Moreover, it is shown that if R is strongly ${\alpha}-semicommutative$ with ${\alpha}(1)=1$ and S is a domain, then the Dorroh extension D of R by S is strongly ${\bar{\alpha}}-semicommutative$.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.10 no.1
• /
• pp.21-26
• /
• 1973

A simple matrix method to analyze the ship's transverse frame ring is proposed. In this approach, the frame ring is treated as a plane frame of uniform slender members. The loadings on the frame consist of buoyancy loads, deck loads and cargo loads. The hatch coaming are considered to deflect under the loads. Because of symmetry, only the half of the frame is analyzed. The method is to obtain the forces and moments on each member. The deformation of the frame can be determined from the nodal displacements. For a sample calculation, a frame ring of a 10,000 ton class cargo liner is analyzed on the IBM 1130 computer. The numerical results obtained are proved to be resonable.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.675-677
• /
• 2018

• Kyungpook Mathematical Journal
• /
• v.60 no.1
• /
• pp.71-72
• /
• 2020

A ring R is quasi-reversible if 0 ≠ ab ∈ I(R) for a, b ∈ R implies ba ∈ I(R), where I(R) is the set of all idempotents in R. In this short paper, we prove that the ring of 2×2 matrices over an arbitrary field is quasi-reversible, which is an answer to the question given by Da Woon Jung et al. in [Bull. Korean Math. Soc., 56(4) (2019) 993-1006].

• Communications of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.1069-1078
• /
• 2019

Let R be a ring with identity and P(R) denote the prime radical of R. An element r of a ring R is called strongly P-clean, if there exists an idempotent e such that $r-e=p{\in}P$(R) with ep = pe. In this paper, we determine necessary and sufficient conditions for an element of a trivial Morita context to be strongly P-clean.

• Journal of applied mathematics & informatics
• /
• v.29 no.5_6
• /
• pp.1603-1608
• /
• 2011

Let R be a ring with identity. If a, b, $c{\in}R$ such that a+b+c = 1, then the distributive laws from addition over multiplication hold in R, that is a+(bc) = (a+b)(a+c) when ab = ba, and (ab)+c = (a+c)(b+c) when ac = ca. An application to obtains, if A,B are idempotent matrices and AB = BA = 0 then there exists an idempotent matrix C such that A + BC = (A + B)(A + C), and also A + BC = (I - C)(I - B). Some other cases and applications are also presented.