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Ring-theory
New post in Ring-theory
The subring criterion
September 22nd, 2020
ring-theory
Find all the ideals of $\mathbb Q[X]$
December 28th, 2020
abstract-algebra
ideals
ring-theory
when does 1 ever equal zero? integral domain question
February 18th, 2020
abstract-algebra
ring-theory
Prove the field of fractions of $F[[x]]$ is the ring $F((x))$ of formal Laurent series.
April 13th, 2020
ring-theory
field-theory
Prove that the characteristic of a finite integral domain $A$ divides the order of $A$
November 11th, 2020
ring-theory
field-theory
group-theory
Vector spaces and multiplicative inverse?
January 27th, 2020
abstract-algebra
ring-theory
vector-spaces
Let R be an integral domain. Show that if the only ideals in R are {0} and R itself, R must be a field
December 8th, 2020
ring-theory
abstract-algebra
Find all ring homomorphisms from $\Bbb Q$ to $\Bbb R$
August 1st, 2022
ring-theory
abstract-algebra
Definition of the subalgebra generated by a set
August 1st, 2022
ring-theory
abstract-algebra
Show that if $M$ is a semisimple artinian module then $M$ is finitely generated.
April 11th, 2020
noetherian
ring-theory
abstract-algebra
modules
Let $R$ be a commutative ring with unity $1$. An element $a \in R$ is called to be nilpotent if $a^n = 0$ for some positive integer $n$
December 1st, 2020
ring-theory
group-theory
abstract-algebra
What is the relationship between prime ideals and their generators?
November 13th, 2020
ideals
ring-theory
abstract-algebra
finitely-generated
maximal-and-prime-ideals
How to find the inverse polynomial in a quotient ring?
September 23rd, 2020
polynomials
ring-theory
ideals
maximal-and-prime-ideals
What are the "units" and "non-trivial divisors of zero" in a ring?
June 5th, 2020
ring-theory
field-theory
divisibility
Length of a ring? Lenth of a (right or left) ideal
August 25th, 2020
abstract-algebra
ideals
ring-theory
Order of an element in an integral domain
August 1st, 2022
ring-theory
integral-domain
abstract-algebra
Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
August 1st, 2022
ring-theory
Intersection of two ideals
April 29th, 2020
ideals
abstract-algebra
proof-verification
ring-theory
Characteristic of a product ring?
August 1st, 2022
ring-theory
abstract-algebra
Show that a ring $R$ is a division ring if and only if, for each nonzero $a\in R$, there is a unique element $b\in R$ such that $aba = a$.
August 1st, 2022
abstract-algebra
ring-theory
Show that for a Noetherian ring R, the R-module R$^{n}$ is Noetherian
August 1st, 2022
ring-theory
modules
How to formally prove that a degree 2 or 3 polynomial f(x) ∈ F[x] is irreducible if and only if it has no root in F
August 1st, 2022
factoring
abstract-algebra
polynomials
ring-theory
field-theory
Proving a Ring is Semi-Primitive
August 1st, 2022
abstract-algebra
ring-theory
Can every ring be embedded in a ring with identity of arbitrary characteristics?
August 1st, 2022
ring-theory
abstract-algebra
Find the inverse of a polynomial in a quotient ring
April 7th, 2021
ring-theory
abstract-algebra
Show that $Q[\sqrt3]$ is a field
August 1st, 2022
field-theory
ring-theory
abstract-algebra
3 different subgroup tests. When to use each? are they all equivalent?
August 1st, 2022
abstract-algebra
group-theory
ring-theory
Nilpotent and Idempotent Elements of Ring $\mathbb{Z}_6 \times \mathbb{Z}_2$
August 1st, 2022
idempotents
ring-theory
abstract-algebra
Algebraic integers form a ring without irreducible elements, every non-zero prime ideal $\ne(0)$ is maximal, ...
August 1st, 2022
algebraic-number-theory
ring-theory
abstract-algebra
Intersection of radical ideal
August 1st, 2022
abstract-algebra
ring-theory
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