• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.181-184
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• 2006

We prove the following results: (1) Let R be a strongly euclidean semiring. Then an ideal A of $R_{n{\times}n}$ is a partitioning ideal if and only if it is a subtractive ideal. (2) A monic ideal M of R[$x$], where R is a strongly euclidean semiring, is a partitioning ideal if and only if it is a subtractive ideal.

• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.69-76
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• 2011

In this paper, we introduce a partitioning ideal of a ternary semiring which is useful to develop the quotient structure of ternary semiring. Indeed we prove : 1) The quotient ternary semiring S/$I_{(Q)}$ is essentially independent of choice of Q. 2) If f : S ${\rightarrow}$ S' is a maximal ternary semiring homomorphism, then S/ker $f_{(Q)}$ ${\cong}$ S'. 3) Every partitioning ideal is subtractive. 4) Let I be a Q-ideal of a ternary semiring S. Then A is a subtractive ideal of S with I ${\subseteq}$ A if and only if A/$I_{(Q{\cap}A)}$ = {q + I : q ${\in}$ Q ${\cap}$ A} is a subtractive idea of S/$I_{(Q)}$.

• 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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.9
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• pp.2145-2152
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• 1993

The objective of this paper is to examine the detection limit, growth characteristics and notch curvature radius in short crack problem. Measurement techniques such as ultrasonic method and back-face strain compliance method were adopted. The fatigue crack growth rate of the short crack is slower than that of a long crack for a notched specimen. The characteristic of crack growth and crack closure is same as the case of a delay of crack growth caused by constant amplitude load for an ideal crack or single peak overload for a fatigue crack. The short crack is detected effectively by ultrasonic method. A short surface crack occurs in the middle of specimen thickness and is transient to a through crack depth is larger than the notch curvature radius.