La scheda
Yuan Dong
Titolo: La grande bellezza (2013)
Regista: Paolo Sorrentino
Personaggi principali:
Jep Gambardella (Toni Servillo);
Romano (Carlo Verdone);
Ramona (Sabrina Ferilli)
Ambientazione:
Math 111C, Spring 2015, Problem (9)
(9) Show that the polynomials X 3 2 and X 3 3 in Q[X] do not have isomorphic
splitting elds over Q.
Proof. First note the following: Every polynomial f Q[X] \ Q has
SUGGESTIONS AND SOME MOTIVATION
FOR REVIEW OF 111B MATERIAL
Prelude, partly doubling up on what I said in class: Whenever we analyze prototypes
of algebraic structures, such as vector spaces, groups,
MATH 111C, S 2015, OVERVIEW
Basics
Denitions. Field, subeld, eld homomorphism, prime eld, characteristic.
Theorem 1. For any eld F , either char(F ) = 0 or char(F ) = p, where p is a positive
prime in
MATH 111C, S 2015, OVERVIEW
Basics
Denitions. Field, subeld, extension eld, eld homomorphism, prime eld, characteristic.
Theorem 1. For any eld F , either char(F ) = 0 or char(F ) = p, where p is a po
KRONECKERS THEOREM, FIRST VERSION
We know: Every embedding : F K of elds induces an embedding of polynomial
rings : F [X] K[X] (i.e., an injective ring homomorphism); it sends any polynomial
d
d
i
i
i
MATH 111C, S 2015, EXISTENCE OF
SPLITTING FIELDS, GENERAL VERSION
Ill start with a reminder. In class, we proved:
Theorem 14 [nite version]. Let F be a eld and P a nite set of nonconstant polynomials
MATH 1110 NAME
SECOND MIDTERM
15 May 2015, 10:0010:50 PERM NO.
PLEASE WRITE NEATLY. When giying proofs, be sure to sort out tentative ideas
on scratch paper, and to put down your argument in a logical
MATH 1 1 1 C NAME
FIRST MIDTERM
24 April 2015, 10:00-10:50 PERM NO.
PLEASE WRITE NEATLY. When giving proofs, be sure to sort out tentative ideas
on scratch paper, and to put down your argument in a lo
Math 111C, Spring 2015, Homework Assignments
All assignments refer to our text, Abstract Algebra, third edition, by Dummit & Foote.
March 30: p.519, # 5
April 1: p.519, # 7, more cleanly stated as fol
MATH 111C, S 2015, OVERVIEW
Basics
Denitions. Field, subeld, eld homomorphism, prime eld, characteristic.
Theorem 1. For any eld F , either char(F ) = 0 or char(F ) = p, where p is a positive
prime in
EMPATHY AND VIOLENCE
1
Empathy and Violence: Connecting Characteristics in Psychopathy and Autism Spectrum
Disorder to Criminal Offenses
My signature below certifies that I have complied with the Univ
In 1922 Benito Mussolini came to power in Italy. To make the capital city a strong symbol of
Fascism, he put forth significant effort into restoring and renovating Rome, with the idea of
transforming
Dong 1
Tristan Dong
Instructor: Mehmet-Ali Ata
ARCH 226 Archaeology of Anatolia
Dec 9, 2015
Assyrian Influences on Pre-classical Anatolia: from the Trading Colony to Urartian Art
The arrival of Old As
Art in Neolithic Anatolia: a Response
Tristan Dong
Oct 3, 2015
During its first survey, limestone slabs of mammoth proportions were discovered in the site of
Gbekli Tepe. Interestingly, these rocks an
A REMARK ON FINITE ABELIAN GROUPS THAT
FEEDS INTO THE PROOF OF THEOREM 22
Auxiliary Proposition. Let A be a nite abelian group. Then there exists an element
x A such that |y| divides |x| for all y A.