• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.721-729
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• 2007

In this paper, we have characterizations of idempotent matrices over general Boolean algebras and chain semirings. As a consequence, we obtain that a fuzzy matrix $A=[a_{i,j}]$ is idempotent if and only if all $a_{i,j}$-patterns of A are idempotent matrices over the binary Boolean algebra $\mathbb{B}_1={0,1}$. Furthermore, it turns out that a binary Boolean matrix is idempotent if and only if it can be represented as a sum of line parts and rectangle parts of the matrix.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.113-123
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• 2009

A rank one matrix can be factored as $\mathbf{u}^t\mathbf{v}$ for vectors $\mathbf{u}$ and $\mathbf{v}$ of appropriate orders. The perimeter of this rank one matrix is the number of nonzero entries in $\mathbf{u}$ plus the number of nonzero entries in $\mathbf{v}$. A matrix of rank k is the sum of k rank one matrices. The perimeter of a matrix of rank k is the minimum of the sums of perimeters of the rank one matrices. In this article we characterize the linear operators that preserve perimeters of matrices over semirings.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.353-365
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• 1994

During the past century, one of the most active and continuing subjects in matrix theory has been the study of those linear operators on matrices that leave certain properties or subsets invariant. Such questions ar usually called "Linear Preserver Problems".

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.213-225
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• 1997

Let A be a real $m \times n$ matrix. The column rank of A is the dimension of the column space of A and the maximal column rank of A is defined as the maximal number of linearly independent columns of A. It is wekk known that the column rank is the maximal column rank in this situation.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.5
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• pp.734-740
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• 2010

We define and study the fuzzy nil radical of a fuzzy ideal of a commutative $\kappa$-semiring.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.107-120
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• 2016

Let R be a commutative semiring. The purpose of this note is to investigate the concept of 2-absorbing (resp., weakly 2-absorbing) primary ideals generalizing of 2-absorbing (resp., weakly 2-absorbing) ideals of semirings. A proper ideal I of R said to be a 2-absorbing (resp., weakly 2-absorbing) primary ideal if whenever $a,b,c{\in}R$ such that $abc{\in}I$ (resp., $0{\neq}abc{\in}I$), then either $ab{\in}I$ or $bc{\in}\sqrt{I}$ or $ac{\in}\sqrt{I}$. Moreover, when I is a Q-ideal and P is a k-ideal of R/I with $I{\subseteq}P$, it is shown that if P is a 2-absorbing (resp., weakly 2-absorbing) primary ideal of R, then P/I is a 2-absorbing (resp., weakly 2-absorbing) primary ideal of R/I and it is also proved that if I and P/I are weakly 2-absorbing primary ideals, then P is a weakly 2-absorbing primary ideal of R.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1037-1046
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• 2023

The reason behind to investigate axiom systems with fewer axioms into investigate what types of results still hold, and what results become more general. Seminearrings obtained by the generalisation of nearrings and semirings. Clearly, seminearrings are common abstraction of semirings and nearrings. The aim of this work is to carry out an extensive study on algebraic structure of seminearrings and the major objective is to further enhance the theory of seminearrings in order to study the special structures of seminearrings, this work addresses some special structures of seminearrings such as right duo seminearrings. The right ideal of a seminearring need not be a left ideal. We focused on those seminear-rings which demonstrate this property. A seminearring S is right duo if every right ideal is two sided. Here we have concentrated on the seminearring which are right duo and regular. Main aim of this paper is to deal with properties of regularity in right duo seminearring. We have given some results on right duo seminearring. Followed by that, we have derived some theorems on the relation between the properties of seminearring such as regularity, semi simplicity and intra-regularity in right duo seminearring. We also illustrate this concept with suitable examples.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.357-365
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• 2006

This paper is a sequel of our previous paper [1]. In this paper, we introduce the notions of regular ideal and partial ideal ($p$-ideal) in a ternary semiring and using these two notions we characterize regular ternary semiring.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.113-123
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• 2014

The term rank of a matrix A over a semiring $\mathcal{S}$ is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to term rank inequalities of matrices over nonbinary Boolean semirings.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.335-342
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• 1996

Suppose $k$ is a field and $M$ is the set of all $m \times n$ matrices over $k$. If T is a linear operator on $M$ and f is a function defined on $M$, then T preserves f if f(T(A)) = f(A) for all $A \in M$.