On Partitioning and Subtractive Ideals of Ternary Semirings

• Journal title : Kyungpook mathematical journal
• Volume 51, Issue 1,  2011, pp.69-76
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2011.51.1.069
Title & Authors
On Partitioning and Subtractive Ideals of Ternary Semirings
Chaudhari, Jaiprakash Ninu; Ingale, Kunal Julal;

Abstract
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/$\small{I_{(Q)}}$ is essentially independent of choice of Q. 2) If f : S $\small{{\rightarrow}}$ S' is a maximal ternary semiring homomorphism, then S/ker $\small{f_{(Q)}}$ $\small{{\cong}}$ 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 $\small{{\subseteq}}$ A if and only if A/$\small{I_{(Q{\cap}A)}}$ = {q + I : q $\small{{\in}}$ Q $\small{{\cap}}$ A} is a subtractive idea of S/$\small{I_{(Q)}}$.
Keywords
Ternary semiring;subtractive ideal;partitioning ideal;quotient ternary semiring;maximal homomorphism;isomorphism;
Language
English
Cited by
1.
On Partitioning and Subtractive Ideals of Ternary Semirings,;;

Kyungpook mathematical journal, 2011. vol.51. 1, pp.69-76
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