Some Results On Symmetric Rings And Reversible Rings

In this paper we mainly study some properties of reversible rings, symmetric rings, group rings and quotient rings which are associative with identity, based on the results given by former papers, the main contents are included as follows:(1) In Chapter 1, as preliminaries, we introduce the basic concepts about reversible rings, reduced rings, symmetric rings and semicommutative rings and also some relevant results about these rings.(2) In Chapter 2, we observe the properties of symmetric rings, and we also study the Trivial, Dorroh and Nagata extensions of symmetric rings.(3) In Chapter 3, we find out the necessary and sufficient condition under which a class of skew group rings is reversible.(4) In Chapter 4, we show that although symmetric Martindale quotient rings preserve the reversibility, the right (left) Martindale quotient rings need not be reversible.