Algebraic algebras over Π-regular rings

On Semiabelian π-Regular Rings

A ring R is defined to be semiabelian if every idempotent of R is either right semicentral or left semicentral. It is proved that the set N(R) of nilpotent elements in a π-regular ring R is an ideal of R if and only if R/J(R) is abelian, where J(R) is the Jacobson radical of R. It follows that a semiabelian ring R is π-regular if and only if N(R) is an ideal of R and R/N(R) is regular, which ex...

Triangulaizability of Algebras Over Division Rings

Algebraic Geometric Codes over Rings

Whenever information is transmitted across a channel, errors are likely to occur. Since Shannon’s groundbreaking paper [36], coding theorists have sought to construct codes that have many codewords, that are easy to encode and decode, and that correct errors. While the main tools used in coding theory have traditionally been those of combinatorics and group theory, this volume is dedicated to c...

Separable Algebras over Commutative Rings

Introduction. The main objects of study in this paper are the commutative separable algebras over a commutative ring. Noncommutative separable algebras have been studied in [2]. Commutative separable algebras have been studied in [1] and in [2], [6] where the main ideas are based on the classical Galois theory of fields. This paper depends heavily on these three papers and the reader should con...

triangulaizability of algebras over division rings