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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.
Undergrad An Embarrassing Question about turning a ring into a module
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Undergrad Spivak's proof of Cauchy Schwarz
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Graduate Is the Injective Hull of an Irreducible Module in Group K?
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High School Please help me, I do not understand this sentence in vector mathematics
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Undergrad Understanding Quotient Groups in Abstract Algebra
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MHB The cofactors of elements for every determinant
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Undergrad Property of Jacobian Determinant
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MHB La1.1.22 3 aug matrices for linear sys solution set is x_1=3,x_2=-2,x_3=-1
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Graduate Proving the Dual of Schanuel's Lemma
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Graduate Construct a unique simple submodule
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MHB What is a Quinary Vector and How is it Related to Matrices?
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High School Can elementary matrix operations change the solutions to a system of equations?
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Undergrad What Are the Symmetry Groups of GL(10, R) and Z?
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Undergrad Rotation of a point in R3 about the y-axis
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High School Can Linear Systems of Equations Have More Than Three Solutions?
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Undergrad Why Does the Proof Assume ##|x| = n## in Finite Cyclic Groups?
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Undergrad Is quintic only polynomial that needs to be proven imposs?
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Undergrad Using group action to prove a set is a subgroup
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MHB Why Is the Containment xR ⊆ x1R Proper in Lemma 4.3.10?
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MHB Two dimensional rotational Matrix
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MHB Why Does \( a_1 \mid b_1 b_2 \cdots b_n \) in Theorem 7.2.20?
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MHB Why Does p|aby' in Theorem 7.2.14?
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MHB Is there a formula that gives me the RREF of a matrix?
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MHB Equation of a plane determined by three or four points in R4
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MHB Why Does y ∈ xR Imply xR = yR in Theorem 3.2.19?
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MHB Solves Theorem 3.2.19 in Bland's Abstract Algebra
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MHB Prime and Maximal Ideals .... Bland -AA - Theorem 3.2.16 .... ....
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Graduate Number Line in Synthetic differential geometry
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MHB Maximal Ideal .... Bland - AA - Example 2, Section 3.2.12 .... ....
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Graduate Does an irreducible representation acting on operators imply....
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MHB Ring vs. Field: Comparing Two Common Sports Venues
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MHB Definition of a Euclidean Domain ....
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MHB Principal Ideal Domains .... ....
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Undergrad Vector that satisfies systems of equations simultaneously
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Undergrad Showing that inverse of an isomorphism is an isomorphism
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Undergrad Showing that every element in G can be written a certain way
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MHB Principal Ideal Rings and GCDs .... .... Bland Proposition 4.3.3
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Undergrad Ways of writing a logical argument
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Undergrad Showing that AxB is isomorphic to BxA
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MHB Jordan-Holder Theorem for Modules .... .... Another Two Questions ....
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MHB Jordan-Holder Theorem for Modules .... ....
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MHB Composition Series and Noetherian and Artinian Modules ....
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Undergrad Showing that two groups are not isomorphic question
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Undergrad Show that commutativity is a structural property
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Undergrad Complete sets and complete spaces
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Undergrad Order of a permutation is the lcm of the orders of cycles
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Undergrad Given order for every element in a symmetric group
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Undergrad Prove that elements of x^i 0<i<n-1 are distinct
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Undergrad Why choose traceless matrices as basis?
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Undergrad Can You Determine the Order of (a,b) in A x B?
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Undergrad Prove that x and x^-1 have same order
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Undergrad Showing that a binary operation is well-defined
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Undergrad Necessary and sufficient x^3=1
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Undergrad How can we use induction to prove the generalized associative law?
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Undergrad What is orientation or shear transform collectively termed?
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Graduate Getting new irreducible representations from old ones
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Undergrad A little problem about quotient modules
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MHB How Does Corollary 4.2.6 Prove M is Noetherian?
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MHB Generation of Modules .... Dummit and Foote, Section 10.3 .... ....
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Undergrad Real function inner product space
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MHB Choose from the following set of vectors in R4
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Undergrad Rings, Modules and the Lie Bracket
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Undergrad How Does Zero Characteristic Influence the Structure of Prime Subfields?
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Undergrad Zero divisors of an endomorphism ring
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MHB Homomorphic Images of Free Modules .... Bland, Proposition 2.2.6 .... ....
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MHB Understanding Bland's Proposition 4.2.10 in Rings and Modules
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MHB Finite Sum of Indecomposable Modules .... Bland, Proposition 4.2.10 .... ....
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Undergrad Is perspective a homothetic transformation?
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MHB Noetherian Modules: Direct Sums & Bland Proposition 4.2.7
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Undergrad A question I have about my L.A. textbook (2)
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MHB How to Prove Corollary 4.2.8 in Noetherian Rings?
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Graduate Differences between Gaussian integers with norm 25
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Undergrad Submodules and Factor Modules of a Noetherian Module ....
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MHB Noetherian Modules, Submodules and Factor Modules .... Problem/Exercise
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MHB Direct Sums of Noetherian Modules .... Bland Proposition 4.2.7 .... ....
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High School Can a matrix be transformed like a vector?
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Undergrad Dyad as a product of two vectors: what does ii or jj mean?
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Undergrad Two Questions I Have About My L.A. Textbook
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MHB Noetherian Modules and Short Exact Sequences .... Bland, Corollary 4.2.6 ....
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MHB Endomorphism Rings .... Bland, Example 7, Section 1.1 .... ....
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MHB Can Submodules of a Noetherian Module Fail to Intersect with a Given Submodule?
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MHB Modules Generated by Sets of Submodules .... .... Bland Problem 2, Problem Set 4.1 .... ....
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Undergrad Outer product in geometric algebra
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MHB R[X] is never a field .... Sharp, Exercise 1.29 .... ....
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MHB Generating/spanning modules and submodules .... .... Blyth Theorem 2.3
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Undergrad Group Theory: Elements as Ops, Representations as Math?
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Undergrad Solve Coin Sum Problem: Find Combinations for 200p
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Undergrad Generating/spanning modules and submodules .... ....
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MHB Generating/spanning modules and submodules .... ....
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Undergrad Generating modules and sub modules Blyth Theorem 2.3
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MHB Artinian Modules - Bland - Proposition 4.24
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MHB How to Solve a Vector Word Problem Involving Airplanes and Wind?
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Graduate A decreasing sequence of images of an endomorphisme
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Graduate Does Closure Under Multiplication in One Subspace Imply the Same for Another?
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MHB Direct Sums and Factor Modules .... Bland Problem 14, Problem Set 2.1
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MHB Max Complex Matrices of Order $n$: $\lfloor n^2/4\rfloor + 1$
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MHB Artinian Modules - Cohn Exercise 3, Section 2.2, page 65
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MHB Start on Bland Problem 1, Problem Set 4.1: Generating & Cogenerating Modules
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Graduate On a finitely generated submodule of a direct sum of modules....
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MHB On a finiteley generated submodule of a direct sum of left R-modules
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