"Discusses the latest results concerning the area of noncommutative ring theory known as the theory of generalized identities (GIs)--detailing Kharchenko's results on GIs in prime rings, Chuang's extension to antiautomorphisms, and the use of the Beidar-Mikhalev theory of orthogonal completion in the semiprime case. Provides novel proofs of existing results."

Polynomial Identities in Ring Theory

This volume consists of seven papers related in various matters to the research work of Kostia Beidar†, a distinguished ring theorist and professor of National Ching Kung University (NCKU). Written by leading experts in these areas, the papers also emphasize important applications to other fields of mathematics. Most papers are based on talks that were presented at the memorial conference which was held in March 2005 at NCKU.

Among all areas of mathematics, algebra is one of the best suited to find applications within the frame of our booming technological society. The thirty-eight articles in this volume encompass the proceedings of the International Conference on Algebra and Its Applications (Athens, OH, 1999), which explored the applications and interplay among the disciplines of ring theory, linear algebra, and coding theory. The presentations collected here reflect the dialogue between mathematicians involved in theoretical aspects of algebra and mathematicians involved in solving problems where state-of-the-art research tools may be used and applied. This Contemporary Mathematics series volume communicates the potential for collaboration among those interested in exploring the wealth of applications for abstract algebra in fields such as information and coding. The expository papers would serve well as supplemental reading in graduate seminars.

This volume showcases mostly the contributions presented at the International Conference in Algebra and Its Applications held at the Aligarh Muslim University, Aligarh, India during November 12-14, 2016. Refereed by renowned experts in the field, this wide-ranging collection of works presents the state of the art in the field of algebra and its applications covering topics such as derivations in rings, category theory, Baer module theory, coding theory, graph theory, semi-group theory, HNP rings, Leavitt path algebras, generalized matrix algebras, Nakayama conjecture, near ring theory and lattice theory. All of the contributing authors are leading international academicians and researchers in their respective fields. Contents On Structure of ∗-Prime Rings with Generalized Derivation A characterization of additive mappings in rings with involution| Skew constacyclic codes over Fq + vFq + v2Fq Generalized total graphs of commutative rings: A survey Differential conditions for which near-rings are commutative rings Generalized Skew Derivations satisfying the second Posner’s theorem on Lie ideals Generalized Skew-Derivations on Lie Ideals in Prime Rings On generalized derivations and commutativity of prime rings with involution On (n, d)-Krull property in amalgamated algebra Pure ideals in ordered Γ-semigroups Projective ideals of differential polynomial rings over HNP rings Additive central m-power skew-commuting maps on semiprime rings A Note on CESS-Lattices Properties Inherited by Direct Sums of Copies of a Module Modules witnessing that a Leavitt path algebra is directly infinite Inductive Groupoids and Normal Categories of Regular Semigroups Actions of generalized derivations in Rings and Banach Algebras Proper Categories and Their Duals On Nakayama Conjecture and related conjectures-Review On construction of global actions for partial actions On 2-absorbing and Weakly 2-absorbing Ideals in Product Lattices Separability in algebra and category theory Annihilators of power values of generalized skew derivations on Lie ideals Generalized derivations on prime rings with involution

This book contains the definitions of several ring constructions used in various applications. The concept of a groupoid-graded ring includes many of these constructions as special cases and makes it possible to unify the exposition. Recent research results on groupoid-graded rings and more specialized constructions are presented. In addition, there is a chapter containing open problems currently considered in the literature. Ring Constructions and Applications can serve as an excellent introduction for graduate students to many ring constructions as well as to essential basic concepts of group, semigroup and ring theories used in proofs.