• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.693-697
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• 2012

In this note, we discuss $N(R,<_R)$-structure in a semiring, and show that if ($R,+,{\cdot}$) is a cancellative $<_+$-stable semiring, then ($R/N(R,<_+),+,{\cdot}$) is a semiring.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.1
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• pp.88-92
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• 2004

In this paper, we define and study the semiprimary k-fuzzy ideals in a commutative k-semiring and characterize the quotient semiring R/A of a k-semiring R by a semiprimary k-fuzzy ideal A. In particular, we show that every zero divisor of R/A is nilpotent.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.4
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• pp.321-330
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• 2006

We introduce the concept of intuitionistic fuzzy weak congruence on a semiring and obtain the relation between intuitionistic fuzzy weak congruence and intuitionistic fuzzy ideal of a semiring. Also we define and investigate intuitionistic fuzzy quotient semiring of a semiring over an intuitionistic fuzzy ideal or over an intuitionistic fuzzy weak congruence.

• Journal of the Chungcheong Mathematical Society
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• v.1 no.1
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• pp.7-9
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• 1988

Using the notion [1] of Q-ideal in a semiring we study some properties, especially g-zero, of quotient semiring.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.3
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• pp.423-429
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• 2007

We define and study the fuzzy Jacobson radical of a ${\kappa}$-semiring. Also it is shown that the Jacobson radical of the quotient semiring R/FJR(R) of a ${\kappa}$-semiring by the fuzzy Jacobson radical FJR(R) is semisimple. And the algebraic properties of the fuzzy ideals FJR(R) and FJR(S) under a homomorphism from R onto S are also discussed.

• 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/$I_{(Q)}$.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.243-249
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• 1998

In this paper, we introduce a congruence relation on a semiring and a quotient semiring, and prove some homomorphism theorems.

• 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.

• Communications of the Korean Mathematical Society
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• v.4 no.1
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• pp.17-22
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• 1989

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.37-44
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• 2013

Let R be a commutative semiring with $1_R{\neq}0_R$. Characterization of subsemimodules, prime subsemimodules and primary subsemimodules which are subtractive extensions of Q-subsemimodules in R-semimodules are investigated.