Elements Definition and 984 Threads

Homework Statement Find, with justification, all the elements of ##\operatorname{Aut} (\mathbb{Z}/4\mathbb{Z})##. Which ones are in ##\operatorname{Inn} (\mathbb{Z} / 4\mathbb{Z})##? Homework EquationsThe Attempt at a Solution First we note that ##\operatorname{id}_{\mathbb{Z} / 4\mathbb{Z}}...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.3: Modules Over Principal Ideal Domains ... and I need some help in order to fully understand the proof of Proposition 4.3.14 ... ... Proposition 4.3.14 reads as follows: In the above proof by Bland we read...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.3: Modules Over Principal Ideal Domains ... and I need yet further help in order to fully understand the proof of Proposition 4.3.14 ... ... Proposition 4.3.14 reads as follows: In the above proof by...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.3: Modules Over Principal Ideal Domains ... and I need some further help in order to fully understand the proof of Proposition 4.3.14 ... ... Proposition 4.3.14 reads as follows: In the above proof by...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.3: Modules Over Principal Ideal Domains ... and I need some help in order to fully understand the proof of Proposition 4.3.14 ... ... Proposition 4.3.14 reads as follows: In the above proof by Bland we...

I want to get a copy of historical Algebra literature that essentially the equivalent of Euclid’s Elements for Algebra. Does anyone have any recommendations?

Homework Statement Homework Equations 3. The Attempt at a Solution [/B] ## |3 \rangle = |1 \rangle - 2 ~ |2 \rangle ## So, they are not linearly independent. One way to find the coefficients is : ## |3 \rangle = a~ |1 \rangle +b~ |2 \rangle ## ...(1) And solve (1) to get the values of a...

I am reading Dummit and Foote's book: "Abstract Algebra" (Third Edition) ... I am currently studying Chapter 10: Introduction to Module Theory ... ... I need some help with an Exercise 8(c) of Section 10.1 ... Exercise 8 of Section 10.1 reads as...

I am reading Dummit and Foote's book: "Abstract Algebra" (Third Edition) ... I am currently studying Chapter 10: Introduction to Module Theory ... ... I need some help with an Exercise 8(b) of Section 10.1 ... Exercise 8 of Section 10.1 reads as follows...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.3: Modules Over Principal Ideal Domains ... and I need some help in order to formulate a proof of Proposition 4.3.5 Part (iii)... ... Proposition 4.3.5 reads as...

Find the cofactors of the elements in the second row of every determinant: $$\begin{vmatrix}-2 & 0 & 1 \\ 1 & 2 & 0 \\ 4 & 2 & 1 \end{vmatrix}$$ I am going to guess that I need to look at each number in the second horizontal row to see what i and j are for finding the cofactors of the elements...

There are 118 elements known to man, and some scientists like Feynman think that element 137 might be the end of the Periodic Table. Isn't that oddly specific? To me, it feels like it is completely random and of no significance. What is going on here? Is there a constant that relates to this...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.3: Modules Over Principal Ideal Domains ... and I need some help to fully understand the proof of Lemma 4.3.10 ... ... Lemma 4.3.10 and its proof read as...

I am reading The Basics of Abstract Algebra by Paul E. Bland ... I am focused on Section 7.2 Euclidean, Principal Ideal, Unique Factorization Domains ... ... I need help with the proof of Theorem 7.2.14 ... ... Theorem 7.2.14 and its proof reads as follows: In the above proof by Bland we...

Homework Statement Explain the following order of the boiling point (° C) HF (19.5)> HCl (-85.1) <HBr (-66.8) <HI (-35.4) b) Explain the following order of connection distance (pm): HF (92) <HCl (127) <HBr (141) <HI (161) Homework Equations xxx The Attempt at a Solution a) HF does hydrogen...

Homework Statement If ##a## and ##b## are commuting elements of ##G##, prove that ##(ab)^n = a^nb^n## for all ##n \in \mathbb{Z}##. Homework EquationsThe Attempt at a Solution We prove two lemmas: 1) If ##a## and ##b## commute, then so do their inverses: ##ab=ba \implies (ab)^{-1} = (ba)^{-1}...

Here is the statement: If x is an element of finite order ##n## in ##G##, prove that the elements ##1,x,x^2, \dots , x^{n-1}## are all distinct. So I started by reinterpreting the question into something more tangible. Is it true that this problem is equivalent to the following? Suppose that...

Find the elements in each set given that: U={1,2,3,4,5,6,7} A={1,3,5,7} B={2,4,6} C={1,2,5,6} D={2,3,4} A) C intersect D B) C-D C) (A union B) union C D) (C union A)' -D

This may be bit weird but really do we get any product after the reaction of 118 elements of the periodic table.We know masses of reactant = masses of product.But no so in nuclear fission and fusion.Anyhow finally what might be that product?and what is going to be its state.Please explain me...

Hi All, I would like to know if the following statement is true or false: The nuclear processes that happen inside the Sun can produce at least one unity of each of the known chemical elements. Best Regards, DaTario

Homework Statement Write out the following set by listing its elements between braces: {X : X ⊆ {3,2,a} and |X| = 4} Homework EquationsThe Attempt at a Solution My book tells me that it is ∅, but couldn't X have repeated elements? so X = {3,2,a,3}, {3,2,a,2} etc for example??

If caesium 133 frequency for its hyperfine structure is 9 192 631 770, and hydrogen is 1 420 405 751.7667 what are the frequencies for the other elements and their isotopes? Is there a list on line some were because this would be a long list. Any help on where to look on line would be...

Homework Statement Determine the Lie bracket for 2 elements of SU(3). Homework Equations [X,Y] = JXY - JYX where J are the Jacobean matrices The Attempt at a Solution I exponentiated λ1 and λ2 to get X and Y which are 3 x 3 matrices.. If the group elements are interpreted as vector...

Been reading basic stuff about the astrophysics behind the prevalence of various elements, curious at what rate this changes over time. The Milky Way is something like 14 billion years old. At first it was all H and He then heavier elements were created and distributed through supernovae...

If we have n object and n1,n2,..nk are identical element. And we take r at a time i.e r < n. Is there a general formulae for the permutation of the above. Or how it is solved? Thanks.

Let me be more specific: I'm needing some source that talks, in a more broad way, about how heavier elements tend to "sink into the core" during Earth's formation (when we're talking about siderophile elements, that readily combine with molten iron). Wikipedia's page about the Goldschmidt...

Hey! C^2_2 = 1\:\:\:C^2_3 = 3\:\:\:C^2_4 = 6\:\:\:C^2_5 = 10 \\ We\:can\:see\:that\:\:\:C^2_n = C^2_{n-1} + (n-1),\:let's\:try\:n = 5 \\ C^2_5 = C^2_4 + (5 - 1) \\ = C^2_3 + (4 - 1) + (5 - 1) \\ = C^2_2 + (3 - 1) + (4 - 1) + (5 - 1) \\ = 1 + (3 - 1) + (4 - 1) + (5 - 1) \\ C^2_5 = (1 - 1) + (2 -...

Homework Statement Write a sequence of statements to REVERSE the elements of array X1. Homework Equations - The Attempt at a Solution Here's my work : Could somebody check my answer please ?

Just a simple and bald question. Is it possible to fuse heavy elements like uranium?. I mean, massive stars core fusion process stops at iron. Please don’t blame me for my lack of scientific rigurosity. Thank you in advance. AGZ

What would be reasonable preparation for reading the reference Kaon Physics https://arxiv.org/pdf/hep-ph/0401236.pdf I find I do not seem to be ready for this reading. I am familiar with quantum mechanics at the level of Schiff (an old text for first year graduate students) though perhaps rusty...

Good day All I have a doubt regarding the derivation of the following matrix according to my basic understanding we want to go from the basis u1 v1 u2 v2 to the basis u'1 v'1 u'2 v'2, and for doing so we use the rotation matrix the rotation matrix is the following and the angle theta is...

$M$ is the set of squares of the first $20$ natural numbers:\[M = \left\{1^2,2^2,3^2,...,19^2,20^2\right\}\]We say that $n$ is a good number, if in any subset of $M$ of size $n$ there are two elements $a$ and $b$ such that $a + b$ is a prime number. Find the smallest good number.

I am practicing for my math exam next week and I came across this problem: A set has 200 elements in it. It is partitioned into three subsets so that the second and third subsets have the same number of elements. If four times the number of elements in the second subset is three times as many...

Sorry for the abbreviation above; character limits, and all. Anyway: 1. Homework Statement "Suppose that ##x∈ℝ## and ##\epsilon>0##. Prove that ##(x-\epsilon,x+\epsilon)## is a neighborhood of each of its members. In other words, if ##y∈(x-\epsilon,x+\epsilon)##, then prove that there is a...

Hello. First post here so hi all. My question(s) is regarding the formation of solar masses by accretion of gases and dust. From what I understand, stars are formed by large clouds of gasses and dust particles pulling together and with enough gravity, (magnetic fields), and time. A fusion...

This might be a very basic question. What are the elements that are in the world of creating covalent bonds, distinguishing themsevels from the elements that never form covalent bonds? Many thanks!

Homework Statement X is the set of all integers n that satisfy the inequality 2 <= |n| <=5 What are the elements of set X? Homework Equations Provided above. The Attempt at a Solution In my view X should have: 2, 3, 4, 5 elements. I can't understand how X have negative values. Some body...

Hello all, I am a senior electrical engineering student at Purdue University and I am working on my senior capstone project. One of the aspects of my project is to measure voltage and current waveforms as well as the relative phase shift between them. I need to get these waveforms into a data...

Homework Statement A silly sample of a metallic element M, reacts completely with 0.0237 mols of X2 to form 6.78 g MX. What are the identities of M and X? Homework Equations mols = grams/molar mass[/B]The Attempt at a Solution (kinda have no clue what to do because I'm not sure what to do...

So the recent neutron star merger event showed that most of the heavy elements (gold, platinum, uranium, etc.) are produced in kilonovas. But with neutron star mergers so rare, there can't be that many kilonovas. Prior to this I always used to think they were mostly produced in supernovas. The...

I have seen it claimed online that the recently announced observation of a neutron-star merger by LIGO provides strong support for the hypothesis that heavy elements - gold and platinum were mentioned in particular - are mostly created in neutron-star collisions rather than in supernovas. Is...

My question might seem simple, however I couldn't find data on this. Let me explain my situation: I'm involved in a project about the formulation of new criteria to avaliate exoplanetary systems for search of extraterrestrial intelligence. The key question is mostly around the element...

Could calcium and copper and say - boron, be joined into one substance? If not boron, then which element? I am trying to design an alien skeleton with copper, calcium, and ? I love copper and part of the idea is its distribution throughout the universe. I am asking for a tip about where to look...

Why is it that all group 15 element's trihalides except Nitrogen on hydrolysis gives an acid while Nitrogen trichloride give ammonia which is a base on hydrolysis?

So, I was wondering when will mining seawater for minerals be affordable. The whole process seems very energy intensive to do. Will it ever be a reality one day where we see tritium and deuterium mined alongside lithium and other important elements? I've read somewhere that there are enough...

SOLVED Hi there. I have the elements of a matrix written in a txt file (in row major order). I need to read this matrix to use it in my fortran77 program. The text file contains the elements written in this way: A(1,1) A(1,2) ... A(1,N) ... A(N,N-1) A(N,N). I was thinking in doing a do loop...

Homework Statement Show that any two Fields with four elements are isomorphic. Homework EquationsThe Attempt at a Solution Let ##F= \{0,1,a,b\}## be a field with four elements. Since ##F## is an additive abelian group, by Lagrange's theorem ##1## must have either an order of ##2## or ##4##...

I have always wanted to read the textbooks in the thread title. But their styld is so old. Does someone know of any "middle of the road" textbooks? By that, I mean: books that basically teach what these two men wrote, but, perhaps with updated language, or some really-not-essential stuff...

Wondering if anybody had information on cooling elements such as coils or plastics?

I have heard that chaos exists in all dynamical systems.Does this mean that chaos exists in circuits with linear elements too?Which software is best for analyzing chaos in electric circuits?