On Certain Aspects of Noncommutative Ring Theory

Abstract algebra can be broadly classified into theory of groups and theory of rings. The theory of rings in turn are studied through two main classes: commutative rings and arbitrary or noncommutative rings. The study of noncommutative rings has always been more challenging in comparison to the study of commutative rings. One of the strongest reasons behind this is that commutative ring theory has huge applicability in the fields of number theory and geometry. In spite of this limitation, noncommutative ring theory certainly enjoys an advantage over its commutative counterpart as it evokes curiosity in researchers to study properties of rings in the possible absence of commutativity. In this book, a sincere attempt has been made to introduce the readers to two of the celebrated classes of noncommutative rings, viz., regular rings and reversible rings.