Skew Armendariz rings and their relations

The theory of rings is of paramount importance in the realm of algebra, as it deals primarily with the structures required to develop other algebraic theories and their applications. The aim of this project is to investigate a class of rings called Armendariz rings, which generalizes fields and integral domains. Armendariz rings play an important role in algebra research and related topics. The concept of the Armendariz ring is useful in understanding the relation between annihilators of ring and its polynomial ring and skew polynomial ring. It must be noted that, throughout this research, all rings are associative with identity unless otherwise specified. The relationships between Armendariz rings and certain other classes of rings shall be dealt with throughout the course of this discussion. Such rings include:Baer and p:p:-ring, abelian and semi-commutative rings, reversible and symmetric rings, as well as others. In addition, the generalizations of Armendariz rings and classical quotient rings will be considered. Moreover, using this properties of a ring to its polynomial and skew polynomial rings will be investigated. These factors impel the author of this discussion to consider the fact that the ring has the property of , as do its polynomial and skew polynomial ring. This research also defines quasi @ Armendariz and quasi @ skew Armendariz ringsand their properties, as well as the quasi-Armendariz properties of Laurent type and power series.

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