An Alternative Approach to the Concept of Separability in Galois Theory
نویسنده
چکیده
The notion of a separable extension is an important concept in Galois theory. Traditionally, this concept is introduced using the minimal polynomial and the formal derivative. In this work, we present an alternative approach to this classical concept. Based on our approach, we will give new proofs of some basic results about separable extensions (such as the existence of the separable closure, Theorem of the primitive element and the transitivity of separability).
منابع مشابه
A History of Selected Topics in Categorical Algebra I: From Galois Theory to Abstract Commutators and Internal Groupoids
This paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical Galois theory and involves generalized central extensions, commutators, and internal groupoids in Barr exact Mal’tsev and more general categories. Galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...
متن کاملDeformation of Outer Representations of Galois Group
To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...
متن کاملConcept and conditions of alternative performance of contractual obligations in Iranian and modern international documents
The approach of modern international documents such as DCFR, PELC, OHADA, UPICC, CISG in fulfilling the obligations is to increase the probability and chance of fulfilling the obligation by the obligor by accepting multiple obligations and the possibility of choosing one obligation by the obligee or the obligee to fulfill the obligation. In a function called the alternative performance of contr...
متن کاملAn Alternative Secondary Goal Approach to Modify Cross Efficiency Evaluation in Data Envelopment Analysis
The cross efficiency evaluation is used to performance measurement of decision making units in data envelopment analysis concept. One of the most important shortcoming of this method is existing alternative optimal solution and therefore, the efficiency scores are not unique. We are going to summarize the pervious models proposed by researchers and suggest an alternative secondary goal approach...
متن کاملSolving a nurse rostering problem considering nurses preferences by graph theory approach
Nurse Rostering Problem (NRP) or the Nurse Scheduling Problem (NSP) is a complex scheduling problem that affects hospital personnel on a daily basis all over the world and is known to be NP-hard.The problem is to decide which members of a team of nurses should be on duty at any time, during a rostering period of, typically, one month.It is very important to efficiently utilize time and effort, ...
متن کامل