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Questions related to Algebra
In high school I just studied the concept of vectors and the dot products. Now, I see more advanced concepts of these, like, norms induced by vector spaces. I want to see why and how these...
02 February 2016 3,592 9 View
Both the Quaternion group and the Quaternion algebra are generated by {-1, i, j, k } such that i² =j² =k² =-1, ij=k, jk=i. My questions are 1) What is the substantial relation between them? 2)...
27 January 2016 1,714 36 View
We know that Q[pi] is not a field, but Q(pi) is. However, is that Q(pi) countable?
12 January 2016 8,329 23 View
PRT - U(n) is cyclic iff n = 1,2,4,pk and 2pk .
02 January 2016 6,270 4 View
I know at least three different ones (based on algebra, analysis and topology). what are others?
01 January 2016 286 4 View
I am currently looking for possible topics for my master thesis.My master is specialized in Algebra, but during my year abroad I had several lectures in Cryptography and would like to do something...
01 January 2016 7,493 1 View
01 January 2016 4,309 37 View
It is well known that the reprensentation dimension of k[x,y]/(x^2,y^2,xy+qyx) is 3, where q is a nonzero element in k. And how to compute the representation dimension of its trivial extension...
01 January 2016 7,753 1 View
My friend is a art student and he was asked from me : what is algebra?? He dont know any things about group or ring &... Suppose he don't know any things about mathematics !!!!!! How can...
01 January 2016 7,828 2 View
01 January 2016 8,747 4 View
01 January 2016 6,074 24 View
Let T=[A B;C D] be a real (m+n)X(m+n) stable matrix with controllable pair (D,C). Choosing such matrices T uniformly at random: What is the probability that the nonsymmetric algebraic Riccati...
21 December 2015 7,256 3 View
Let q be an odd positive integer, and let Nq denote the number of integers a such that 0 < a < q/4 and gcd(a, q) = 1. How do I see that Nq is odd if and only if q is of the form pk with k a...
12 December 2015 2,732 4 View
f(t) = (a+A*sin(wt + c))/(b+A*cos(wt + c)) d/dt atan(f(t)) = w (a,b,c,w,A are constants) t = time ______________________________ Numeric Simulation can show validty of the shown equality. The way...
12 December 2015 1,158 3 View
In the algebraic formulation of Quantum Mechanics, how do probability amplitudes naturally arise?
12 December 2015 10,076 4 View
09 December 2015 3,959 3 View
02 December 2015 1,535 2 View
Suppose that G is a finite group and P is a Sylow p-subgroup of G, and H/K is a chief factor of G, and T/K is a Sylow p-subgroup of H/K. Is that correct to say that c(T/K) is less than or equal to...
30 November 2015 4,131 3 View
I want to know about the relations among them.
11 November 2015 6,196 4 View
11 November 2015 2,151 3 View
The same set of unbalanced cycles should be considered up to isomorphism.
09 November 2015 2,333 2 View
I was looking for examples of first order sentences written in the language of fields, true in Q (field of rational numbers) and C (field of complex numbers) but false in R (field of real...
10 October 2015 8,239 46 View
I is an injective module S is submodule of I E is a maximal essential extension of A
10 October 2015 3,826 0 View
09 October 2015 8,588 45 View