ﻻ يوجد ملخص باللغة العربية
In this paper we generalize the definition of rationalizability for square roots of polynomials introduced by M. Besier and the first author to field extensions. We then show that the rationalizability of a set of field extensions is equivalent to the rationalizability of the compositum of the field extensions, providing a new strategy to prove rationalizability of sets of square roots of polynomials.
Feynman integral computations in theoretical high energy particle physics frequently involve square roots in the kinematic variables. Physicists often want to solve Feynman integrals in terms of multiple polylogarithms. One way to obtain a solution i
Let $k$ be a perfect field of characteristic $p>0$, $k(t)_{per}$ the perfect closure of $k(t)$ and $A$ a $k$-algebra. We characterize whether the ring $Aotimes_k k(t)_{per}$ is noetherian or not. As a consequence, we prove that the ring $Aotimes_k k(
Our goal is to determine when the trivial extensions of commutative rings by modules are Cohen-Macaulay in the sense of Hamilton and Marley. For this purpose, we provide a generalization of the concept of Cohen-Macaulayness of rings to modules.
We study when $R to S$ has the property that prime ideals of $R$ extend to prime ideals or the unit ideal of $S$, and the situation where this property continues to hold after adjoining the same indeterminates to both rings. We prove that if $R$ is r
Free extensions of commutative Artinian algebras were introduced by T. Harima and J. Watanabe. The Jordan type of a multiplication map $m$ by a nilpotent element of an Artinian algebra is the partition determining the sizes of the blocks in a Jordan