Nakayama (Ann. of Math. 42, 1941) showed that over an artinian serial ring every module is a direct sum of uniserial modules. Hence artinian serial rings have the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals. A ring with the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals will be called a ...

Let I be a non-zero left ideal of r-ring M satisfying the condition alpha b beta c= c for all a,b,c, e and alpha, r. We show that contains non-trivial central if is semiprime which admits an appropriate derivations on I, also commutative prime admitting centralizing derivation I. next give some characterizations when generalized act as homomorphisms anti-homomorphisms or two-sided ideals gamma ...

We compute the kth power-sum polynomials (for k > 0) over an arbitrary finite ring R, obtained by summing the kth powers of (T + r) for r ∈ R. For R non-commutative, this extends the work of Brawley–Carlitz–Levine [Duke Math. J. 41], and resolves a conjecture by Fortuny Ayuso, Grau, Oller-Marcén, and Rúa (2015). For R commutative, our results bring together two classical programs in the literat...

Abstract For a not-necessarily commutative ring $R$ we define an abelian group $W(R;M)$ of Witt vectors with coefficients in -bimodule $M$ . These groups generalize the usual big rings and prove that they have analogous formal properties structure. One main result is $W(R) := W(R;R)$ Morita invariant -linear endomorphism $f$ finitely generated projective -module characteristic element $\chi _f ...

Authentication is a process by which an entity, which could be a person or intended computer, establishes its identity to another entity. In private and public computer networks including the Internet, authentication is commonly done through the use of logon passwords. Knowledge of the password is assumed to guarantee that the user is authentic. Internet business and many other transactions req...