On an Isomorphism Criterion for Semi-Maximal Rings

The book presents in an introductory way the basic concepts of the theory of semimaximal rings, emphasizing a criterion of isomorphisms. Firstly, some classical ring themes are studied, where we find concepts and examples without further depth of: local rings, rings of fractions, simple rings, semiprimes rings, semi-perfect rings, together with the notion of poset and reticulum necessary for future chapters. Secondly, the theory of discrete valuation rings is shown in a little more detail, and finally, semi-maximal rings are discussed, specifying in the grid of irreducible modules and the poset of projective irreducible modules, with which, at the end of the text, the criterion of isomorphisms of interest is tested.