A Study Of N-absorbing Ideals Of Commutative Semirings,Noether Semirings And Artin Semirings

The ideals and congruences are important contents in semiring algebraic theory.In this dissertation,we mainly study the n-absorbing ideals,and the congruence lattice of Noether and Artin semirings The main results as follows:Firstly,we introduce and study n-absorbing ideals of commutative semir-ings,and characterize the n-absorbing ideals of(max,min)-semiring,(Z+,·,+)and other types of special commutative semirings.In particular,we characterize the n-absorbing ideals of the arbitrary direct product of a family of commutative semirings.Secondly,according to the characterization of congruence lattice of commu-tative semirings,we introduce and study Noether and Artin semirings,then give several equivalent conditions of Noether and Artin semirings.In particular,the left reductive congruences of Noether and Artin semirings are characterized.