Details

Autor(en) / Beteiligte

• Adillah, Aisyah Nur
• Hasnani, Fitriana
• Fatimah, Meryta Febrilian
• Puspita, Nikken Prima

Titel

The Ideal Over Semiring of the Non-Negative Integer

Ist Teil von

• JTAM (Jurnal Teori dan Aplikasi Matematika) (Online), 2023-07, Vol.7 (3), p.743-750

Ort / Verlag

Universitas Muhammadiyah Mataram

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Assumed that (S,+,.) is a semiring. Semiring is a algebra structure as a generalization of a ring. A set I⊆S is called an ideal over semiring S if for any α,β∈I, we have α-β∈I and sα=αs∈I for every s in semiring S.  Based on this definition, there is a special condition namely prime ideal P, when for any αβ∈P, then we could prove that α or β are elements of ideal P. Furthermore, an ideal I of S is irreducible if Ia is an intersection ideal from any ideal A and B on S, then I=A or I=B. We also know the strongly notion of the irreducible concept. The ideal I of S is a strongly irreducible ideal when I is a subset of the intersection of A and B (ideal of S), then I is a subset of A, or I is a subset of B. In this paper, we discussed the characteristics of the semiring of the non-negative integer set. We showed that pZ^+ is an ideal of semiring of the non-negative integer Z^+ over addition and multiplication. We find a characteristic that 〖pZ〗^+  is a prime ideal and also a strongly irreducible ideal of the semiring Z^+ with p is a prime number.