A study on characterizations of T semirings

Abstract

In this thesis, some algebraic characterizations of certain classes of T semirings are studied. First, the concept of regular T-semirings is discussed. Then the notation of commuting regular T-semirings is introduced and some properties about these structures are determined. A necessary and suTcient condition for T-semirings to possess commuting regularity is also obtained. Next, the concept of inverse T-semirings and some results of inverse T-semirings are discussed. Homomorphisms on inverse T-semirings are also determined. The notion of orthodox T semirings and some characterizations of orthodox T-semirings are discussed. Homomorphisms on orthodox T- semirings are also determined. The notions of pseudo symmetric ideals in T-semirings and pseudo symmetric T-semirings are introduced. A class of T-semirings known as semipseudo symmetric T-semiring is investigated. Finally, necessary conditions for semipseudo symmetric T-semirings to possess semisimple elements are obtained and maximal ideals in Archimedian semipseudo symmetric T-semirings are characterized.