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New posts in ring-theory
Under what conditions will the ring homomorphism $\phi : R \to S$ satisfy the following results about prime and maximal ideals?
abstract-algebra
ring-theory
maximal-and-prime-ideals
ring-homomorphism
Does a homomorphism from a unital ring to an integral domain force a multiplicative identity?
ring-theory
Algebras that are free modules over a subalgebra
abstract-algebra
ring-theory
commutative-algebra
The ring $\mathbb{C}[x,y]/\langle xy \rangle$
abstract-algebra
ring-theory
Show that $(2+i)$ is a prime ideal
abstract-algebra
ring-theory
Exhibit the ideals of $\mathbb{Z}[x]/(2,x^3+1)$
abstract-algebra
ring-theory
ideals
polynomial-rings
Why define vector spaces over fields instead of a PID?
ring-theory
vector-spaces
principal-ideal-domains
Commutative integral domain with d.c.c. is a field [duplicate]
abstract-algebra
commutative-algebra
ring-theory
In a matrix ring, no zero divisors may have an inverse
linear-algebra
ring-theory
Do both versions (invariant and primary) of the Fundamental Theorem for Finitely Generated Abelian Groups hold at the same time?
abstract-algebra
group-theory
ring-theory
modules
abelian-groups
Showing two polynomial rings over $\mathbb{C}$ aren't isomorphic
abstract-algebra
polynomials
ring-theory
How to prove $e^{A \oplus B} = e^A \otimes e^B$ where $A$ and $B$ are matrices? (Kronecker operations)
linear-algebra
abstract-algebra
group-theory
ring-theory
quantum-mechanics
Can we make an integral domain with any number of members?
ring-theory
Problem in the "proof" of Eisenstein's criterion on irreducibility.
abstract-algebra
ring-theory
irreducible-polynomials
Prove that $I \subseteq R$ is prime if and only if $R/I$ is an integral domain.
abstract-algebra
ring-theory
$\exists x \in R$ and $\exists n \in\mathbb{N}$ such that $x^{n+1} = x^n \implies x^2 = x$
abstract-algebra
ring-theory
Show that $(p,\sqrt{d})$ is a prime ideal in $Z[\sqrt{d}]$
ring-theory
algebraic-number-theory
maximal-and-prime-ideals
Suppose R is a commutative ring, M is the maximum ideal of R, and R/M is not a field. Prove: (R/M)² = 0.
abstract-algebra
ring-theory
Characterize finite dimensional algebras without nilpotent elements
abstract-algebra
ring-theory
noncommutative-algebra
Consequence of Nakayama Lemma's to Local Rings
ring-theory
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