What is Abstract: Definition and 532 Discussions

Abstract expressionism is a post–World War II art movement in American painting, developed in New York City in the 1940s. It was the first specifically American movement to achieve international influence and put New York at the center of the Western art world, a role formerly filled by Paris. Although the term "abstract expressionism" was first applied to American art in 1946 by the art critic Robert Coates, it had been first used in Germany in 1919 in the magazine Der Sturm, regarding German Expressionism. In the United States, Alfred Barr was the first to use this term in 1929 in relation to works by Wassily Kandinsky.

View More On Wikipedia.org
Recent contents Top users
  1. X

    Abstract Algebra Problem involving the ideals

    Homework Statement Let f:R→S be a homomorphism of rings. If J is an ideal in S and I={r∈R/f(r)∈J}, prove that I is an ideal in R that contains the kernal of f. Homework Equations The Attempt at a Solution I feel like I have the problem right, but would like to have someone look...
  2. X

    Abstract Algebra Problem involving the order of groups

    Homework Statement Let G be a group with identity e. Let a and b be elements of G with a≠e, b≠e, (a^5)=e, and (aba^-1)=b^2. If b≠e, find the order of b. Homework Equations Maybe the statement if |a|=n and (a^m)=e, then n|m. Other ways of writing (aba^-1)=b^2: ab=(b^2)a...
  3. X

    Abstract Algebra Problem using the division algorithm

    Homework Statement Apply the division algorithm for polynomials to find the quotient and remainder when (x^4)-(2x^3)+(x^2)-x+1 is divided by (2x^2)+x+1 in Z7. Homework Equations The Attempt at a Solution I worked the problem and got that the quotient was (4x^2)-3x-1 and the...
  4. S

    Abstract Algebra Question: order, stabilizer, and general linear groups

    The question asks: 3) Let X be the set of 2-dimensional subspaces of F_{p}^{n}, where n >= 2. (a) Compute the order of X. (b) Compute the stabilizer S in GL_{n}(F_{p}) of the 2-dimensional subspace U = {(x1, x2, 0, . . . , 0) ε F_{p}^{n} | x1, x2 ε F_{p}}. (3) Compute the order of S. (4)...
  5. J

    Abstract Algebra - Properties of Q/Z

    Homework Statement Prove that the group Q/Z under addition cannot be isomorphic to the additive group of a commutative ring with a unit element, where Q is the field of rationals and Z is the ring of integers. Homework Equations The tools available are introductory-level group theory and...
  6. I

    Is Abstract Algebra practical?

    I hear a lot that group theory is important to condensed matter physics. Does it have any practical use? Like if I were to do industry work in materials, would I ever use it? Is it important enough to take a full course on abstract algebra?
  7. L

    Abstract Algebra: Ring Isomorphism Construction

    Homework Statement Homework Equations The Attempt at a Solution
  8. X

    Abstract algebra question concerning center of a group

    Homework Statement If a is the only element of order 2 in a group G, prove that a is an element of Z(G). [Z(G) is the notation used by the book for center of group G] Homework Equations Z(G)={a is an element of G: ag=ga for every g that is an element of G} The Attempt at a...
  9. C

    What are the elements of each order in D_n+Z_9 for n = 7 and 11?

    Pick a number n which is the product of 2 distinct primes 5 or more. Find the number of elements of each order in the groupd D(sub)n+Z(sub)9, completely explaining your work. Verify that these number add up to the order of the group. Ive used 7 and 11 as my primes. So now do I use these...
  10. O

    Abstract algebra , intersection of ideals

    Homework Statement prove that <x^m> intersection <x^n> = <x^LCM(m,n)> Homework Equations The Attempt at a Solution ===> let b be in <x^n> intersection <x^m> then for some t,k,p in Z, b=x^(mt) = x^(nk) thus b=x^(LCM(m,n) * p i.e. b is in <x^LCM(m,n)> <=== let b be...
  11. 2

    Abstract Algebra Question dealing with Constructible Numbers

    Homework Statement Let c=cos(2pi/5). It can be shown that (4c^2)+(2c)-1=0. Use this fact to prove that a 72degree angle is constructible. Homework Equations The Attempt at a Solution I can see that using the equation and what c equals that you get the statement 0=0 and I know...
  12. O

    Practicality of Abstract Algebra

    well the title itself seems to be a paradox, but, What are some applications of abstract algebra (like groups, fields, and rings)? Apparently this determines the symmetry of particles in physics but what are some real-life, money-making application of group theory? (Yes, I money is one of my...
  13. J

    Abstract Algebra Questions .

    Abstract Algebra Questions... I have two problems that I'm a little puzzled by, hopefully someone can shed some light. 1) Show that if H and K are subgroups of the group G, then H U K is closed under inverses. 2) Let G be a group, and let g ε G. Define the centralizer, Z(g) of g in G to...
  14. B

    Matrix of a Linear Transformation (Abstract)

    I was taught that the columns of a matrix, T, representing a transformation represent the first vector space's basis set and the rows represent the basis set of the range vector space. i.e. T(v_k) = t_1,k*w_1 +... + t_(m,k)*w_m So v_k would be the k-th basis vector of the first space, V...
  15. J

    This abstract algebra problem seems trivially easy. Did I overlook something?

    Homework Statement The problem seems too easy so I suspect that I am overlooking something important. A problem this easy would be completely out of character for my professor...
  16. P

    Looking for funny abstract paper

    I'm trying to look for papers with funny abstracts (in particular, there is one I saw a while ago, I believe it was physics, that had an abstract that only said no which I am trying to find, but I would love to see other funny one as well.)
  17. B

    Abstract Algebra - Cyclic groups

    (This is my first post on PF btw - I posted on this another thread, but I'm not sure if I was supposed to) I was doing some practice problems for my exam next week and I could not figure this out. Homework Statement Suppose a is a group element such that |a^28| = 10 and |a^22| = 20...
  18. B

    Abstract Algebra - Cyclic groups

    1. Problem: Suppose a is a group element such that |a^28| = 10 and |a^22| = 20. Determine |a|. I was doing some practice problems for my exam next week and I could not figure this out. (This is my first post on PF btw) 2. Homework Equations : Let a be element of order n in group and let k...
  19. J

    Abstract Algebra Proof: Groups

    Abstract Algebra Proof: Groups... A few classmates and I need help with some proofs. Our test is in a few days, and we can't seem to figure out these proofs. Problem 1: Show that if G is a finite group, then every element of G is of finite order. Problem 2: Show that Q+ under...
  20. D

    Schools Can I take Abstract Algebra as a High School Student?

    I've read up a little bit about Abstract Algebra and it seems like a really interesting subject. A university near me will offer an intro class in it next semester. Trouble is, the university requires Calc III as a prerequisite for the course. I'm taking AP Calc right now at school, but it...
  21. Pythagorean

    Explaining Apparent Superluminal Neutrino Speeds as Quantum Weak Measurement

    Title: Can apparent superluminal neutrino speeds be explained as a quantum weak measurement? Abstract: Probably not http://arxiv.org/abs/1110.2832
  22. J

    This abstract problem appears not to have enough information.

    I've put the problem and my attempt all in one image. I would show the above using induction. But to show the order of the element in question, we need to know what power to raise the element to such that it equals the identity. I feel like the problem is missing information about the...
  23. J

    Using the fact that G is abelian in this abstract algebra problem

    I'll post the problem and my attempt at solution all in one picture: In the red step, I'm using commutative multiplication. Am I allowed to do this? I'm not sure, because the subset of G might not be a subgroup, so I don't know if its necessarily abelian like G is. Or does the fact...
  24. S

    Abstract Algebra: Subgroup Proof

    Homework Statement Show that if H is a subgroup of G and K is a subgroup of H, then K is a subgroup of G. Homework Equations The Attempt at a Solution Well I know that H is a subgroup of G if H is non empty, has multiplication, and his inverses. So I assume that K is a subgroup...
  25. L

    Interface and abstract class definition / difference

    So my understanding is an abstract class is one with at least one abstract method ( ie cannot be executed). It can therefore not bei nstantiated (not entirely sure what instantiated means) An interface I am a bit more confused about. first of all i thought it was where unrelated objects...
  26. ElijahRockers

    PSAT abstract inequality question.

    p<q, r<s, and r<q. Which of the following statements must be true? I. p<s II. s<q III. r<p The correct answer could be either one statement, a combination of statements, or none of the statements. Came across this question while helping some high school students prepare for their SATs...
  27. I

    Abstract Algebra - Subgroup of Permutations

    Homework Statement A is a subset of R and G is a set of permutations of A. Show that G is a subgroup of S_A (the group of all permutations of A). Write the table of G. Onto the actual problem: A is the set of all nonzero real numbers. G={e,f,g,h} where e is the identity element...
  28. C

    Abstract Algebra dihedral group

    Homework Statement Let G be a finite group and let x and y be distinct elements of order 2 in G that generate G. Prove that G~=D_2n, where |xy|=n. I have no idea how to solve this or even where to begin. I tried setting up G=<x,y|x^2=y^2=1=(xy)^n> But couldn't get any farther, I am so...
  29. U

    Abstract Algebra: GCD proof

    Homework Statement If (a,c) = 1 and (b,c) = 1, prove that (ab,c) = 1. Note that (x,y) refers to the greatest common divisor between x and y. 2. The attempt at a solution There is a theorem that says since (a,c) = 1, there exist integers u and v such that au + cv = 1. Likewise, there...
  30. A

    Abstract Algebra: Quotienting and the First Isomorphism Theorem

    Homework Statement Let T be a subset of S and consider the subset U(T)={f \in A(S) | f(t)\inT for every t\inT}. 1) If S has n elements and T has m elements, how many elements are there in U(T)? 2) Show that there is a mapping F:U(T) -> Sm such that F(fg)=F(f)F(g) for f,g\inU(T) and F is onto...
  31. D

    Angle on abstract metric space, has sense?

    Hello, I was wondering if if has any sense of talking about angles on an arbitrary http://en.wikipedia.org/wiki/Metric_space" (where only a distance function with some properties is defined) At first sight it seems to not has any sense, only some metric spaces has angles, namely does that...
  32. A

    Does one need to know elementary number theory to study Abstract Algebra?

    It's been some time that I've been studying abstract algebra and now I'm trying to solve baby Herstein's problems, the thing I have noticed is that many of the exercises are related to number theory in someway and solving them needs a previous knowledge or a background of elementary number...
  33. A

    A problem from Herstein's Abstract algebra

    Homework Statement if f \in Sn show that there is some positive integer k, depending on f, such that fk=i. (from baby Herstein). The Attempt at a Solution Suppose that S={x1,x2,...,xn}. Elements of Sn are bijections from S to S. to show that fk=i it's enough to show that fk(xm)=xm for every...
  34. J

    I'm not sure if this simple first day Abstract Algebra exercise is correct

    Prove: If x has a right inverse given by a and a left inverse given by b, then a = b.The Attempt at a Solution One thing that bothers me: how can we even talk about a left inverse or a right inverse without establishing that x is in an algebraic structure? I wrote this in my proof but I'm not...
  35. M

    Abstract Algebra Proof: gcd(s,t)=r and st=r+v

    Homework Statement Let r,s,t and v be integers with r>0. If st=r+v and gcd(s,t)=r, then gcd(v,t)=r Homework Equations Just stumped. I am not sure what to do next.The Attempt at a Solution There are 2 integers d and e such that S=dR and T=eR, and 2 integers a and b such that Sa+Tb=R. I know I...
  36. N

    Can you recommend me to a book in Abstract Algebra and pre-requistes ?

    Can you recommend me to a book in Abstract Algebra and pre-requistes ?
  37. F

    Proving R[x] is a Principal Ideal Domain Implies R is a Field

    Homework Statement Let R be an integral domain and suppose that R[x] is a principal ideal domain. Show that R is a field. Homework Equations I don't know where to start, I'm not familiar with this material. I was browsing through an abstract algebra book and found this. Would like...
  38. M

    Abstract Algebra: Is It Too Difficult for Calculus?

    Currently I am reviewing basic algebra, trigonometry and I will also be starting calculus this fall semester... I enjoy reading about math and I wanted to know what abstract algebra is? Would this be to difficult to read seeing that I am only starting calculus? If so what other types of...
  39. BloodyFrozen

    Number Theory, Linear & Abstract Algebra

    Are there any basic prerequisites before learning about these branches of mathematics?
  40. B

    Modern Algebra &amp; Real Analysis: Learn Proofwriting?

    Hello, I just took ordinary diff eq and I've had calc III and linear algebra, but I'm worried about taking Modern Algebra or Real Analysis next semester because I have no experience writing proofs. The linear algebra class was all computation on tests and homework (we did see some proofs on...
  41. I

    What is the identity element in abstract algebra groups?

    The .pdf can be ignored. Let A + B = (A - B) U (B - A) also known as the symmetric difference. 1. Look for the identity and let e be the identity element A + e = A (A - e) U (e - A) = A Now there are two cases: 1. (A - e) = A This equation can be interpreted as removing from A all elements...
  42. Z

    Courses Which should I take: Abstract Algebra vs 4th year lab (non-thesis) course?

    I am undecided between these two for 2012 spring term (my last semester hopefully)
  43. matqkks

    Exploring Abstract Vector Spaces: Applications and Intuitive Examples

    I first introduce the vector along the lines 'something with magnitude and direction'. Later on the definition of a vector becomes generic - 'an element of a vector space'. Euclidean spaces (n=2 and n=3) are something we can all visualize. However when describing other vector spaces such as...
  44. P

    Abstract Algebra question

    Homework Statement Let G be a group with pk elements, where p is a prime number and k is greater than or equal to 1. Prove that G has a subgroup of order p. The Attempt at a Solution I attempted to prove this by showing that the conditions for a set to be subgroup form a subgroup of order p...
  45. J

    Use of I vs we in abstract

    Use of "I" vs "we" in abstract I'm writing an abstract for a poster which I am required to give for a fellowship. In general it is my understanding that no one would use "I" in an abstract, even if he or she were the sole author. But in this case, the purpose of the poster session is to...
  46. T

    Is Re-taking Abstract Algebra Necessary for a Strong Foundation in Mathematics?

    I really feel dissapointed in myself that I didn't perform as well as I wanted last semester. I took Modern Algebra I and Geometry. The Geometry class covered Euclidean and non-Euclidean geometries. I bombed the final but earned an overall of a B+ because of a 90-something percentile homework...
  47. B

    Schools Transition to (abstract) university mathematics.

    Hello everyone. I am graduating high school in about a few days (yay!). I'm going to enter university this fall, majoring in math. I just want a few advice on what to do this summer to prepare myself for college mathematics. How can I prepare myself to tackle abstract math, without any prior...
  48. MathWarrior

    Where is abstract algebra used?

    I've been studying cryptography and I found out that AES uses Galois Fields. I was therefore wondering where else does abstract algebra pop-up for real world use?
  49. K

    Best Techniques for Efficient Math Learning in Today's World

    In today's world its not enough just to learn things. You have to be able to learn them fast or you will never accomplish very much. Mathematics can of course be quite difficult to wrap your head around at times and so if one can learn mathematics quickly and efficiently then there are few...
  50. F

    Grad textbook on abstract algebra

    What is the absolute best abstract algebra book for graduate students? I was wanting a book that covers algebra in the most comprehensive manner possible, at about the level of Hungerford's Algebra. I was wondering if Carstensen's Abstract Algebra in the Sigma Series in Pure Mathematics is a...
Back
Top