Algebraic structures provide a comprehensive framework for understanding systems governed by operations such as addition and multiplication. In this context, noncommutative rings—where the order of ...

Transactions of the American Mathematical Society, Vol. 359, No. 2 (Feb., 2007), pp. 827-857 (31 pages) We discuss some of the basic ideas of Galois theory for commutative S-algebras originally ...

Algebraic number theory is a foundational branch of mathematics that investigates the properties of algebraic numbers and their relationships through the lens of field extensions and rings of integers ...

Let $L$ be a finite dimensional Lie algebra over a field $k$ of characteristic zero, $D(L)$ the quotient division ring of $U(L)$. It is shown that the weights of the ...