Join experts in discussing linear and abstract algebra topics. This includes vector spaces and linear transformations. Also groups and other algebraic structures along with Number Theory.
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Graduate Forcing conditions in a solution of an under-determined system
- Telemachus
- · Replies 2 ·
Proving irreducible elements are prime in PIDs
- Math Amateur
- · Replies 16 ·
How to Find the GCD and LCD in Mathematics?
- karush
- · Replies 3 ·
D&F section 10.1 exercise 8(c) on torsion elements
- Math Amateur
- · Replies 1 ·
Join the MA104 College Algebra Forum at Lehman College
- mathdad
- · Replies 2 ·
Is \( n! > 2^n \) for \( n \ge 4 \)?
- karush
- · Replies 4 ·
Undergrad Vectorizing tensor product of probability distributions
- Prez Cannady
- · Replies 3 ·
Matrix solutions with variable coefficient
- TheFallen018
- · Replies 1 ·
Undergrad How to interpret a ring as a module over itself
- TMO
- · Replies 3 ·
Undergrad Spivak's proof of Cauchy Schwarz
- e-pie
- · Replies 6 ·
Graduate Is the Injective Hull of an Irreducible Module in Group K?
- TMO
- · Replies 5 ·
High School Please help me, I do not understand this sentence in vector mathematics
- physicophysiology
- · Replies 3 ·
Undergrad Understanding Quotient Groups in Abstract Algebra
- Wledig
- · Replies 8 ·
The cofactors of elements for every determinant
- Tonia1
- · Replies 6 ·
Undergrad Property of Jacobian Determinant
- Gear300
- · Replies 2 ·
La1.1.22 3 aug matrices for linear sys solution set is x_1=3,x_2=-2,x_3=-1
- karush
- · Replies 9 ·
Graduate Proving the Dual of Schanuel's Lemma
- TMO
- · Replies 7 ·
Graduate Construct a unique simple submodule
- TMO
- · Replies 1 ·
What is a Quinary Vector and How is it Related to Matrices?
- Sudharaka
- · Replies 6 ·
High School Can elementary matrix operations change the solutions to a system of equations?
- opus
- · Replies 10 ·
Undergrad What Are the Symmetry Groups of GL(10, R) and Z?
- Mr Davis 97
- · Replies 18 ·
Undergrad Rotation of a point in R3 about the y-axis
- NatFex
- · Replies 6 ·
High School Can Linear Systems of Equations Have More Than Three Solutions?
- opus
- · Replies 29 ·
Undergrad Why Does the Proof Assume ##|x| = n## in Finite Cyclic Groups?
- Mr Davis 97
- · Replies 9 ·
Undergrad Is quintic only polynomial that needs to be proven imposs?
- swampwiz
- · Replies 2 ·
Undergrad Using group action to prove a set is a subgroup
- Mr Davis 97
- · Replies 1 ·
Why Is the Containment xR ⊆ x1R Proper in Lemma 4.3.10?
- Math Amateur
- · Replies 3 ·
Two dimensional rotational Matrix
- cbarker1
- · Replies 3 ·
Why Does \( a_1 \mid b_1 b_2 \cdots b_n \) in Theorem 7.2.20?
- Math Amateur
- · Replies 3 ·
Why Does p|aby' in Theorem 7.2.14?
- Math Amateur
- · Replies 4 ·
Is there a formula that gives me the RREF of a matrix?
- Rorschach
- · Replies 2 ·
Equation of a plane determined by three or four points in R4
- Rorschach
- · Replies 2 ·
Why Does y ∈ xR Imply xR = yR in Theorem 3.2.19?
- Math Amateur
- · Replies 2 ·
Solves Theorem 3.2.19 in Bland's Abstract Algebra
- Math Amateur
- · Replies 1 ·
Why does n₁n₂ ∈ pℤ imply n₁ or n₂ in pℤ?
- Math Amateur
- · Replies 2 ·
Graduate Number Line in Synthetic differential geometry
- Srr
- · Replies 6 ·
Is 5Z a maximal ideal of Z in Bland's proof?
- Math Amateur
- · Replies 3 ·
Graduate Does an irreducible representation acting on operators imply....
- hideelo
- · Replies 3 ·
Differences between ring and field in algebra
- roni1
- · Replies 4 ·
Two definitions of Euclidean domains: Bland vs Dummit and Foote
- Math Amateur
- · Replies 2 ·
Proof of Lemma 7.2.13 on principal ideal domains
- Math Amateur
- · Replies 2 ·
Undergrad Vector that satisfies systems of equations simultaneously
- Telemachus
- · Replies 9 ·
Undergrad Showing that inverse of an isomorphism is an isomorphism
- Mr Davis 97
- · Replies 3 ·
Undergrad Showing that every element in G can be written a certain way
- Mr Davis 97
- · Replies 1 ·
Why does d = a₁R + a₂R + ... + aₙR imply each aᵢ is in (d)?
- Math Amateur
- · Replies 1 ·
Undergrad Ways of writing a logical argument
- Mr Davis 97
- · Replies 1 ·
Undergrad Showing that AxB is isomorphic to BxA
- Mr Davis 97
- · Replies 1 ·
Jordan-Holder theorem: maximal submodules and artinian modules
- Math Amateur
- · Replies 1 ·
Jordan-Holder theorem: why does M₁ + N₁ = M when N₁ is maximal?
- Math Amateur
- · Replies 2 ·
Why is a simple R-module both artinian and noetherian?
- Math Amateur
- · Replies 3 ·
Undergrad Showing that two groups are not isomorphic question
- Mr Davis 97
- · Replies 1 ·
Undergrad Show that commutativity is a structural property
- Mr Davis 97
- · Replies 1 ·
Undergrad Complete sets and complete spaces
- cromata
- · Replies 2 ·
Undergrad Order of a permutation is the lcm of the orders of cycles
- Mr Davis 97
- · Replies 5 ·
Undergrad Given order for every element in a symmetric group
- Mr Davis 97
- · Replies 2 ·
Undergrad Prove that elements of x^i 0<i<n-1 are distinct
- Mr Davis 97
- · Replies 3 ·
Undergrad Why choose traceless matrices as basis?
- phoenix95
- · Replies 1 ·
Undergrad Can You Determine the Order of (a,b) in A x B?
- Mr Davis 97
- · Replies 1 ·
Undergrad Prove that x and x^-1 have same order
- Mr Davis 97
- · Replies 1 ·
Undergrad Showing that a binary operation is well-defined
- Mr Davis 97
- · Replies 5 ·
Undergrad Necessary and sufficient x^3=1
- Mr Davis 97
- · Replies 4 ·
Undergrad How can we use induction to prove the generalized associative law?
- Mr Davis 97
- · Replies 3 ·
Undergrad What is orientation or shear transform collectively termed?
- swampwiz
- · Replies 1 ·
Graduate Getting new irreducible representations from old ones
- hideelo
- · Replies 2 ·
Undergrad A little problem about quotient modules
- steenis
- · Replies 12 ·
How Does Corollary 4.2.6 Prove M is Noetherian?
- Math Amateur
- · Replies 10 ·
Sum of submodules equals submodule generated by union in Dummit and Foote 10.3
- Math Amateur
- · Replies 4 ·
Undergrad Real function inner product space
- Mr Davis 97
- · Replies 6 ·
Choose from the following set of vectors in R4
- forzi
- · Replies 4 ·
Undergrad Rings, Modules and the Lie Bracket
- nigelscott
- · Replies 10 ·
Undergrad How Does Zero Characteristic Influence the Structure of Prime Subfields?
- Danijel
- · Replies 2 ·
Undergrad Zero divisors of an endomorphism ring
- Danijel
- · Replies 1 ·
Proof of Proposition 2.2.6 on homomorphic images of free modules
- Math Amateur
- · Replies 1 ·
Understanding Bland's Proposition 4.2.10 in Rings and Modules
- Math Amateur
- · Replies 4 ·
Bland's Proposition 4.2.10: finite sums of indecomposable modules
- Math Amateur
- · Replies 1 ·
Undergrad Is perspective a homothetic transformation?
- swampwiz
- · Replies 7 ·
Short exact sequences with direct sums in Bland's Proposition 4.2.7
- Math Amateur
- · Replies 9 ·
Undergrad A question I have about my L.A. textbook (2)
- StoneTemplePython
- · Replies 6 ·
How to Prove Corollary 4.2.8 in Noetherian Rings?
- Math Amateur
- · Replies 6 ·
Graduate Differences between Gaussian integers with norm 25
- Ventrella
- · Replies 2 ·
Undergrad Noetherian module submodules and factor modules in Proposition 4.2.5
- Math Amateur
- · Replies 13 ·
Proving M is Noetherian when N and M/N are Noetherian
- Math Amateur
- · Replies 21 ·
Why is each Mi isomorphic to a submodule of the direct sum in Bland 4.2.7?
- Math Amateur
- · Replies 2 ·
High School Can a matrix be transformed like a vector?
- snoopies622
- · Replies 2 ·
Undergrad What does ii or ij mean in dyad notation?
- Sorcerer
- · Replies 7 ·
Undergrad Two Questions I Have About My L.A. Textbook
- gibberingmouther
- · Replies 6 ·
Proving Corollary 4.2.6 on Noetherian modules in Bland
- Math Amateur
- · Replies 9 ·
Why Z subscript in End_Z(G) notation for group homomorphisms
- Math Amateur
- · Replies 2 ·
Can Submodules of a Noetherian Module Fail to Intersect with a Given Submodule?
- Math Amateur
- · Replies 2 ·
Bland's problem on modules generated by submodules
- Math Amateur
- · Replies 66 ·
Undergrad Outer product in geometric algebra
- Silviu
- · Replies 8 ·
Proving R[X] is never a field using polynomial degree arguments
- Math Amateur
- · Replies 2 ·
Linear combinations in Blyth Theorem 2.3 on generating submodules
- Math Amateur
- · Replies 1 ·
Undergrad Group Theory: Elements as Ops, Representations as Math?
- kent davidge
- · Replies 7 ·
Undergrad Counting non-negative integer solutions to linear Diophantine equations
- Arman777
- · Replies 13 ·
Undergrad Reconciling Dauns and Bland's definitions of generated modules
- Math Amateur
- · Replies 5 ·
Reconciling Dauns and Bland's definitions of generated modules
- Math Amateur
- · Replies 2 ·
Undergrad Generating modules and sub modules Blyth Theorem 2.3
- Math Amateur
- · Replies 3 ·
Artinian Modules - Bland - Proposition 4.24
- Math Amateur
- · Replies 7 ·
How to Solve a Vector Word Problem Involving Airplanes and Wind?
- Gummg
- · Replies 3 ·