Let $f\colon A\to B$ be an injective homomorphism of associative rings. It induces the faithful functor $F\colon B\text{-mod} \to A\text{-mod}.$ Are there any known conditions on $f$ for $F$ to be full (i.e. the $B$-mod is a full subcategory of $A$-mod)?
2025-01-13 02:15:26.1736734526
Fully-faithful functors between categories of modules
269 Views Asked by Boris Bilich https://math.techqa.club/user/boris-bilich/detail AtRelated Questions in ABSTRACT-ALGEBRA
- Projective Indecomposable modules of quiver algebra
- Binary relations for Cobb-Douglas
- Relations among these polynomials
- Number of necklaces of 16 beads with 8 red beads, 4 green beads and 4 yellow beads
- Page 99 of Hindry's Arithmetics, follows from exact sequence that $\text{N}(IJ) = \text{N}(J)\text{card}(J/IJ)$?
- How to write the identity permutation as a product of transpositions
- Is $H$ a subgroup?
- $x=(0,\overline{1})$ and $y=(0,\overline{2})$ generate the same ideal in $R=\mathbb{Z}\times\mathbb{Z}/5\mathbb{Z}$
- Having some problems with understanding conics and graphing (eccentricity)
- Is this Cayley Diagram contradictory?
Related Questions in RING-THEORY
- $x=(0,\overline{1})$ and $y=(0,\overline{2})$ generate the same ideal in $R=\mathbb{Z}\times\mathbb{Z}/5\mathbb{Z}$
- Show that the quotient ring $R/\mathcal{I}$ is a field.
- Prime ideals $\mathfrak{p} \supset \mathfrak{a}$ are finite in one-dimensional Noetherian domain
- Constructing finite fields of order $8$ and $27$ or any non-prime
- How do I show that the unit group of $\mathbb{Z}\times\mathbb{Z}/5\mathbb{Z}$ is a cyclic group of order 10?
- What is a cubic ideal/partial cubic ideal?
- Surjective ring homomorphism from polynomial to complex numbers
- Generalization of nilpotency in ring theory?
- Give an example of an injective ring homomorphism $f : R \to S$ where $R$ is commutative, but $S$ is not commutative
- Is the ring of formal power series in infinitely many variables a unique factorization domain?
Related Questions in CATEGORY-THEORY
- Are there right-deformations for abelian sheaves?
- Category Theory compared with Meta-Grammars (or Hyper-Grammars) in Programming Languages
- over categories of a morphism?
- Epimorphic morphisms of sheaves
- Finite Limits, Exponentiation and Sub-Object Classifiers imply Finite Co-Limits
- What is a nice "naturally occurring" example of an arrow category?
- $G$-sets, natural correspondence?
- Finitely generated iff direct limits of subobjects are bounded by subobjects
- Is there a different term for the "left-regular representation" of categories?
- Category theory: Are all composable arrows actually arrows?
Related Questions in MODULES
- Proper essential extensions
- If module $M = N + mM$, then why is $m(M/N) = M/N$?
- On the invariance of basis number
- Geometric intuition for coherent rings, modules, and sheaves
- Finitely generated iff direct limits of subobjects are bounded by subobjects
- Finding highest weight of a $gl(3)$ submodule of a $gl(4)$-module
- A simple Congruence Equation
- On the $R$-linear independence of free $R$-module
- Do all submodules of $R^n$ have a complement in $R^n$?
- Formulas give irreducible representation, $SL(2, \mathbb{C})$.
Related Questions in FUNCTORS
- FInitary functors-a definition
- Riehl's Category Theory in Context - Exercise 1.5.vii without Axiom of Choice
- Fully-faithful functors between categories of modules
- Ordinary presheaf as $\infty$-presheaf
- Structure of triangulated category generated by category $B-$mod, where $B=A/J$
- What is the image of the empty category under a given functor?
- Relation between monomorphicity and faithfulness?
- Prove Hom reflects exactness without applying Yoneda
- How does one define constant functor of simplicial sets?
- Is there a notion of polynomial ring in "one half variable"?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity