Abstract

In this paper, we generalize the concept of the full -ideals of a semiring to ternary semiring and prove that the set of zeroids annihilator of a right ternary semimodule, and the Jacobson radical of a ternary semiring are all full -ideals of. Also we prove that the set of all full -ideals of a ternary semiring is a complete lattice which is also modular.

Highlights

  • The notion of a ternary semiring was first introduced by T

  • They define the notion of a right ternary semimodule over a ternary semiring and Jacobson radical of a ternary semiring in [2]

  • Consider full k-ideals of a semiring and they prove that the set of all full k-ideals of a semiring is a complete lattice which is modular and they discussed several characterizations of k-ideals of a semiring

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Summary

Introduction

The notion of a ternary semiring was first introduced by T. They define the notion of a right ternary semimodule over a ternary semiring and Jacobson radical of a ternary semiring in [2]. R. Adhikari, consider full k-ideals of a semiring and they prove that the set of all full k-ideals of a semiring is a complete lattice which is modular and they discussed several characterizations of k-ideals of a semiring. The present paper extends some results of [3] to a ternary semirings

Preliminary Definitions
Full k-ideal
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