## What is/are Weakly Prime?

Weakly Prime - Moreover, we study the notions of prime, weakly prime, semiprime and weakly semiprime ideals of an ordered n-ary semigroup.^{[1]}Lately, the prime submodules were generalized into weakly prime submodules and almost prime submodules.

^{[2]}Furthermore, we introduce the concepts of prime, weakly prime and semiprime fuzzy hyperideals of ordered $$*$$ -semihypergroups.

^{[3]}In this paper, we introduce the concept of weakly S-prime ideals which is a generalization of weakly prime ideals.

^{[4]}We define the notions of prime, semiprime, weakly prime and weakly semiprime properties of one-sided ordered ideals of ordered semirings, study their connections and use them to characterize several kinds of regularities on ordered semirings.

^{[5]}

## weakly 2 prime

A proper ideal P of A is said to be a weakly 2-prime ideal if whenever for some then or Besides giving various examples and characterizations of weakly 2-prime ideals, we investigate the relations between weakly 2-prime ideals and other classical ideals such as 2-prime ideals, weakly prime ideals and weakly 2-absorbing primary ideals.^{[1]}

## Graded Weakly Prime

In this article, we consider the structure of graded rings, not necessarily commutative nor with unity, and study the graded weakly prime ideals.^{[1]}Furthermore, we show that graded 2-prime ideals and graded weakly prime ideals are also different.

^{[2]}Then we introduce the concept of graded weakly S-prime ideals which is a generalization of graded weakly prime ideals.

^{[3]}This class of graded submodules is a generalization of graded weakly prime submodules.

^{[4]}

## Called Weakly Prime

A positive integer [Formula: see text] is called weakly prime-additive if [Formula: see text] has at least two distinct prime divisors and there exist distinct prime divisors [Formula: see text] of [Formula: see text] and positive integers [Formula: see text] such that [Formula: see text].^{[1]}In this paper, we present a new notion of fuzzy ideals : called weakly prime fuzzy ideal.

^{[2]}

## weakly prime ideal

In this article, we consider the structure of graded rings, not necessarily commutative nor with unity, and study the graded weakly prime ideals.^{[1]}Furthermore, we show that graded 2-prime ideals and graded weakly prime ideals are also different.

^{[2]}In this paper, we introduce the concept of weakly S-prime ideals which is a generalization of weakly prime ideals.

^{[3]}Then we introduce the concept of graded weakly S-prime ideals which is a generalization of graded weakly prime ideals.

^{[4]}A proper ideal P of A is said to be a weakly 2-prime ideal if whenever for some then or Besides giving various examples and characterizations of weakly 2-prime ideals, we investigate the relations between weakly 2-prime ideals and other classical ideals such as 2-prime ideals, weakly prime ideals and weakly 2-absorbing primary ideals.

^{[5]}A proper ideal $P$ is said to be weakly prime ideal of $R$ if for every $0\neq ab\in P$ where $a,b\in R,$ implies $a\in P$ or $b\in P$.

^{[6]}As an example, we study the weakly prime ideal elements of a $\vee e$-semigroup and their role to the different type of semigroups mentioned above.

^{[7]}

## weakly prime submodule

Lately, the prime submodules were generalized into weakly prime submodules and almost prime submodules.^{[1]}We introduce the dual notions of S(N)-weakly prime submodules, that is, S(0)-weakly second submodules in a commutative ring with identity.

^{[2]}This class of graded submodules is a generalization of graded weakly prime submodules.

^{[3]}

## weakly prime fuzzy

In this paper, we present a new notion of fuzzy ideals : called weakly prime fuzzy ideal.^{[1]}The notions of the weakly prime fuzzy ideals and three weakly fuzzy m0(m1,m2)-systems of semirings are introduced.

^{[2]}