Article in press
Authors:
Sampad Das
Department of Mathematics
Jadavpur University
Kolkata-700032, India
email: jumathsampad@gmail.com
Manasi Mandal
Department of Mathematics
Jadavpur University
Kolkata-700032, India
email: manasi_ju@yahoo.in
Title:
On 1-absorbing prime and weakly 1-absorbing prime ideals of semirings
PDFSource:
Discussiones Mathematicae - General Algebra and Applications
Received: 2024-08-02 , Revised: 2024-09-01 , Accepted: 2024-09-02 , Available online: 2025-10-01 , https://doi.org/10.7151/dmgaa.1491
Abstract:
In this study, we introduce the concept of 1-absorbing prime ideals
and weakly 1-absorbing prime ideals of commutative semirings with non-zero
identity. A proper ideal I of a commutative semiring S is said to be a 1-absorbing
(resp. a weakly 1-absorbing) prime ideal if whenever abc ∈ I (resp. 0 \neq abc ∈ I)
for some non-units a, b, c ∈ S, then either ab ∈ I or c ∈ I. The relationships
among 1-absorbing prime ideals, prime ideals, 2-prime ideals, and 2-absorbing
ideals are investigated. 1-absorbing prime ideals of the subtractive valuation domain
are studied. Many properties, results, and characterizations of 1-absorbing prime
(resp. weakly 1-absorbing prime) ideals are given.
Keywords:
semiring, 1-absorbing prime ideals, weakly 1-absorbing prime ideals, 2-prime ideals
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https://doi.org/10.1142/S0219498821501759
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