• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.559-573
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• 2006

In this Paper three different types of fuzzy Prime ideals are introduced. Condition is obtained for a fuzzy 2-prime ideal will have two elements in its range. It has been shown that A is fuzzy 2-prime ideal of the semiring R if and only if 1-A is a fuzzy $m_2-system$ in R.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1043-1056
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• 2008

The spanning column rank of an $m{\times}n$ matrix A over a semiring is the minimal number of columns that span all columns of A. We characterize linear operators that preserve the sets of matrix ordered pairs which satisfy multiplicative properties with respect to spanning column rank of matrices over semirings.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.669-679
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• 2022

We provide a characterization of the positive monoids (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.77-86
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• 2006

We consider the set of commuting pairs of matrices and their preservers over binary Boolean algebra, chain semiring and general Boolean algebra. We characterize those linear operators that preserve the set of commuting pairs of matrices over a general Boolean algebra and a chain semiring.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.110-114
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• 2009

We introduce the concepts of intuitionistic fuzzy k-ideals and intuitionistic fuzzy prime k-ideals of a semiring. And we investigate some properties of them.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.169-178
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• 2007

We consider the set of $n{\times}n$ idempotent matrices and we characterize the linear operators that preserve idempotent matrices over Boolean algebras. We also obtain characterizations of linear operators that preserve idempotent matrices over a chain semiring, the nonnegative integers and the nonnegative reals.

• Kyungpook Mathematical Journal
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• v.20 no.2
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• pp.279-280
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• 1980

• Kyungpook Mathematical Journal
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• v.26 no.2
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• pp.129-135
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• 1986

• Kyungpook Mathematical Journal
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• v.17 no.1
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• pp.21-29
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• 1977

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.221-233
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• 2009

In this article, we generalize a well-known result of Hebisch and Weinert that states that a finite semidomain is either zerosumfree or a ring. Specifically, we show that the class of commutative semirings S such that S has nonzero characteristic and every zero-divisor of S is nilpotent can be partitioned into zerosumfree semirings and rings. In addition, we demonstrate that if S is a finite commutative semiring such that the set of zero-divisors of S forms a subtractive ideal of S, then either every zero-sum of S is nilpotent or S must be a ring. An example is given to establish the existence of semirings in this latter category with both nontrivial zero-sums and zero-divisors that are not nilpotent.