Clean Like Semiring Notions and Trivial Semiring Extension
Jamal, Sondos Osama Hussain
جامعة النجاح الوطنية
Suppose that S is a commutative semiring with unity different than zero and M an S-semimodule. In this thesis, we study the algebraic and the ideal theoretic properties of SαM, where SαM denotes the trivial semiring extension (or the expectation of S), providing an analog results to the proved ones in the ring situation. In this thesis, different elements like units, zero divisors and other elements of SαM as well as the special ideals like subtractive ideals, prime ideals and other types of ideals of SαM will be identified. The generalization of some of the clean like notions into the semiring situation will be investigated; this thesis also examines some of their properties and the transfer of these notions in the trivial semiring extension. This thesis also provides an application of semirings in classification system which is considered an important technique in data mining which used to assign every element to specific groups based on the similarities between the referred to elements.