On J-semicommutative Rings

Ring theory is an important branch of algebra. This thesis mainly extended two kinds of special classes of rings:semicommutative rings and reversible rings. In terms of the Jacobson radical, we introduced two new classes of rings. We got several results on these new rings. This article is composed of the following components:Part Ⅰ:We introduced the background and development process of semicomm-utative rings, and give some important results in the literature.Part Ⅱ:We introduced some essential known results which was frequently used in the sequel.Part Ⅲ:We extended semicommutative rings and defined a new one called J-semicommutative ring. The main results are the following:A ring is J-semicommutative if and only if the trivial extension is J-semicommutative if and only if Dorr oh extension or Na.ga.ta extension is J semicommutative if and only if so is the power series ring of R. It was showed that if R/J(R) is a semicommutative ring, then R is a J-semicommutative ring. Then we extended the links between semicommutetive rings and reversible rings to J-semicommutetive rings and get some interesting properties of such rings.Part Ⅳ:We defined J*-reversible rings by promoting reversible rings. and characterize such rings from many views. We also did some research on the relationship between J-semicommutetive rings and J*-reversible rings.Part Ⅴ:Given a summary about the properties of two types of rings that were introduced in this article, we investigated the links between them, and roughly forecasted the possible applications and research in the future.