Some results on 1-absorbing prime ideals of commutative semirings

‎Ranote, H. K.

doi:10.22124/jart.2026.29872.1772

Some results on 1-absorbing prime ideals of commutative semirings

Articles in Press

Document Type : Research Paper

Author

H. K. ‎Ranote

Department of‎ ‎Mathematics‎, ‎Maharaja Agarsen University, (Baddi) Solan‎, ‎India

10.22124/jart.2026.29872.1772

Abstract

The main objective of this paper is to study the concept of 1-absorbing prime ideals in commutative semirings as a generalization of 1-absorbing prime ideals in commutative rings‎. ‎We examine several characterizations and examples of 1-absorbing prime ideals and also investigate the 1-absorbing Prime Avoidance Theorem for such ideals‎. ‎Moreover‎, ‎we study the concept of 1-absorbing primary ideals in commutative semirings and studying a method for constructing 1-absorbing primary ideals that are not necessarily primary ideals‎. ‎Finally‎, ‎we examine various characterizations and examples of 1-absorbing primary ideals in commutative semirings‎.

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