Further remarks on $z$-ideals of semirings

Ahmed Maatallah; Amartya Goswami

Further remarks on $z$-ideals of semirings

Ahmed Maatallah, Amartya Goswami

Abstract

In this note, we revisit certain results from a previous work of the second author concerning $z$-ideals of semirings. We demonstrate that the assumption of the semiring being a bzi-semiring can be dispensed with. Additionally, we propose a revised definition of the $z$-radical that enables a more general formulation of results from the earlier work.

Further remarks on $z$-ideals of semirings

Abstract

In this note, we revisit certain results from a previous work of the second author concerning

-ideals of semirings. We demonstrate that the assumption of the semiring being a bzi-semiring can be dispensed with. Additionally, we propose a revised definition of the

-radical that enables a more general formulation of results from the earlier work.

Paper Structure (6 theorems, 4 equations)

This paper contains 6 theorems, 4 equations.

Key Result

Theorem 1

An ideal $\mathfrak{p} \subseteq S$ is $z$-prime if and only if it is a prime $z$-ideal.

Theorems & Definitions (15)

Theorem 1
proof
Remark 2
Lemma 3
proof
Proposition 4
proof
Definition 1
Lemma 5
proof
...and 5 more