abstract-algebra

  1. Hilbert scheme of $n$ point action, torus action fixed points

  2. Is $\mathbb{R}[x]/(x^2+1) \cong \mathbb{C}$?
  3. Does anyone know a simple proof for the fundamental theorem of finitely generated abelian group?
  4. Problem of invariants of binary forms of degree $d$

  5. Another proof for Cayley-Hamilton theorem for modules by means of induction on the number of generators
  6. Factor of polynomial ring
  7. If $A[X] \cong B[X]$ as rings, are the degrees of irreducible polynomials the same in $A$ and in $B$?
  8. K is a subgroup of G. Determine whether the given cosets are disjoint or identical

  9. The multiplicative group $ \mathbb {{F}^{\times}_{7}}$ is isomorphic to a subgroup of multiplicative group $ \mathbb {{F}^{\times}_{31}}$
  10. An Example in Finite Group Theory

  11. Is this a valid proof for why all modules over a field are projective?
  12. How to find closed form or numerical solution to general power fit equation?
  13. Statements about normal operator

  14. Finding all unitary ring homomorphisms
  15. Proof that an automorphism of an extension field of $\mathbb Q$ fixes rationals

  16. Why is the algebra product $A\otimes A\to A$ well defined, given that we know the product $A\times A\to A$?

  17. True or False: For any transposition $(a, b) \in S_p$ such that $1 \le a < b \le p$, it follows that $(b-a, p) = 1$.
  18. Ideal class group of $ \mathbb{Z}[ \sqrt{2} ] $

  19. Explicit concrete examples of k-affinoid algebras

  20. Prove that a finite abelian group contains an element of order $m$ if and only if $m$ divides $n_1$.

  21. About roots for 5 degree polynomial

  22. If $G$ is a group of order $p^5,$ is $C_G(g)$ a normal subgroup of $G,$ where $g \in G \setminus G^{'}.$

  23. What specific algebraic properties are broken at each Cayley-Dickson stage beyond octonions?

  24. Question has fallen in Net-JRF exam?
  25. Are the groups $\mathbb C^\times \times \mathbb R^ \times$ and $\mathbb R^ \times\times \mathbb R^ \times$ isomorphic?
  26. Degree of field extensions in $\mathbb{Q}$ with two algebraic elements

  27. isomorphism of two semigroups
  28. Problem 20 from Herstein's book

  29. Generators of a simple extension K over F

  30. What is a necessary condition to form a set of basis?
  31. Prove that if in ring $R$ multiplications $xy$ and $yx$ are invertible, then elements $x$ and $y$ are also invertible.

  32. A question on maximal subgroups of a finite group.
  33. Irreducible factors of polynomial $X^{p^n}-X$ over $\mathbb{F}_{p^i}[X]$
  34. How many surjective homomorphisms from $\mathbb{Z}^2$ to $\mathbb{Z}/3\mathbb{Z}$?

  35. $G$ has a copy of $G/N$

  36. G is a group and H is a subgroup of G. Find the index of...
  37. Prove that in a Euclidean domain $R$, if a condition is satisfied then $x$ is a unit
  38. Is $1+2\sqrt{-2}$ an irreducible element of $\mathbb{Z}[\sqrt{-2}]$? Is it prime?

  39. Testing a polynomial's reducibility
  40. Show that a certain quotient is indecomposable
  41. Prove these subrings are ideals

  42. Proving formula involving Euler's totient function

  43. Find two subrings S and T such that S + T is not a subring
  44. The alternating group An

  45. Describe all prime and maximal ideals of $\mathbb{Z}_n$

  46. Are there algebraic objects in which "associativity" holds only up to some finite $n$?
  47. Difference between algebraic semantics and algebraization of a logic

  48. Rules for divisibility based on digit sum in general basis.

  49. Identify the ring $\mathbb {Z}[i]/(2 + i) $

  50. spin projector in inverted matrix

  51. Is there a group containing two subgroups: H with 6 elements and K with 10, such that $|H\cap K| = 1$?

  52. Isomorphism between field and polynomial ring over the field

  53. Proving irreducibility
  54. Is a subrepresentation just a subspace, or a representation itself?

  55. Let A be an $m \times n$ matrix, using matrix algebra prove that
  56. Let $f(x)=x^3+x^2+1$ be a cyclotomic polynomial in $Z[x]$? is it a maximal Ideal??

  57. List all equivalence classes of associate elements of $\mathbb{Z}_{12}$

  58. Claim in polynomial division in $R[x,y]$
  59. Can this be considered as an operation over a quotient ring?
  60. In which of the cases $F = \mathbb{Z}_2$ or $F = Q$ the quotient ring $F[x]/(x^2+3)$ is a field
  61. Prove that any element of this group ring is an associate to an element of the polynomial ring and that the group ring is an integral domain
  62. Cardinality of quotient ring $\mathbb{Z_6}[X]/(2X+4)$

  63. Number of elements in the quotient ring $\mathbb{Z}_6 [x]/\langle 2x +4\rangle$

  64. Ring $\frac{\mathbb{Z}}{ \mathbb{6Z}}[x] / \langle 2x+4 \rangle\cong\ ?$
  65. For this ring homomorphism, show that $\ker f$ is a principal ideal and find an element that generates it

  66. Can I prove some thing about dihedral group in term of it subgroup of permutation group?

  67. What is the result of effecting permutation $(124)$ on $\{1, 2, 3, 4, 5, 6\}$?

  68. If $Gal(f/\mathbb{Q}) \cong S_n$ then $Gal(f/\mathbb{Q}(\alpha_1)) \cong S_{n-1}$?

  69. If every prime ideal is maximal, what can we say about the ring?

  70. Commutator subgroup of finite $p$-group of order $p^{n}$ with nilpotency class $n-1.$

  71. How to show that these derived functors are equivalent?

  72. the number of roots of $f∈R[x]$(R is integral domain) is at most n
  73. Given $C$ a field, $f$ a polynomial in $C[x]$ and $I = (f)$, describe $C[x]/I$
  74. A semigroup in which both the equations ax=b and ya=b have unique solution, is a group. Prove it.
  75. Help With Proof of Theorem 1.A. in "Topics in Algebra"
  76. Finding equivalent submodular function
  77. Inverse of a Particular Matrix help R-{0}
  78. Is $\alpha=3-\sqrt[5]{5}-\sqrt[5]{25}$ algebraic over $\mathbb{Q}$?

  79. Prove that there is unique group of order 35 up to isomorphism
  80. How to compute the abelian group $\text{Ext}_{\mathbb{Z}}^{n}(\mathbb{Z} / {a}\mathbb{Z} , \mathbb{Z} / b{\mathbb{Z}})$?

  81. Definition of equivalence of polynomial under a F[x] where is F is a field.

  82. Rational canonical form of diagonal matrix
  83. Should I take Real Analysis and Abstract Algebra together?

  84. Prve that $x^4+x^2+x+1$ is irreducible over $\mathbb{Q}$.

  85. Prove that a group of order $132=11\cdot 12$ has a normal subgroup of order 11 or a normal subgroup of order 12.

  86. Are all polynomials of degree 1 irreducible?

  87. Classification of cyclic Galois extensions
  88. Is maximal unramified extension with a lifting of the residue field fixed under automorphism?

  89. Describe all abelian groups of order 24 up to isomorphism
  90. If $K$ is a field, prove the polynomial ring $K[x]$ has infinitely many maximal ideals.

  91. Showing that $\mathbb{D}=\{ \frac{p}{10^n}\mid p \in \mathbb{Z}, n \in \mathbb{N} \}$ is a principal ideal domain.

  92. Prove that an ideal in $C[x]$ is a max ideal
  93. Functions on a cover with the property $f(U \cap V) = f(U)\,f(V)$

  94. Find the sum and product of $f(x)=3x-5, g(x)=2x^2-4x+3$ in $Z_8$.

  95. I want to prove that there is a group $G$ of order $p^{3}$ satisfying $|a|=p^{2},\,|b|=p \,and\, b^{-1}ab=a^{1+p}$

  96. Group rings of elementary Abelian p-groups over finite fields
  97. A problem of central simple algebras: why $(E,s,\gamma)\cong M_n(F)$ only if $\gamma$ is the norm of an element of $E$?
  98. If $G$ is a non-abelian group of order $p^{3}$ for prime p , then the center of $G$ is generated by all elements of the form $aba^{-1}b^{-1}.$
  99. Action of $SL_2\left(\mathbb{Z}\right)$ on $\mathbb{RP}^1$ is minimal

  100. Understanding Quotient of a Quotient Ring