Newbetuts

If $A$ is generated as a $B$-algebra by $x_i$ and relations $r_j$, then $\Omega_{A/B}$ is generated over $A$ by $dx_i$ subject to $dr_j$.

Ideal products and calculating with ideals

Proof of the single factor theorem over an arbitrary commutative ring

Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal

Error in proof: $\mathbb{C} \cong \mathbb{C} \times \mathbb{C}$??

Prove that the set $a+b\sqrt{2}$ where a and b are rational without zero is a group under multiplication [duplicate]

Understanding the ideal $IJ$ in $R$ [duplicate]

$\mathbb Z [X] / (X)$ isomorphic to $\mathbb Z[X] / (X+1)$ isomorphic to $\mathbb Z [X] / (X+2015)$

Associative ring with identity, inverses, divisors of zero and Artinianity

An example of a Ring with many zero divisors

Inverse of a complex number (in Hamilton's pair representation)

Endomorphisms of modules satisfying chain conditions and counterexamples.

$R$ is an algebra over an infinite field. If $\exists$ ideals s.t. $J\subseteq \bigcup_{k=1}^nI_k$ then $J\subseteq I_k$ for some $k$

In an Integral Domain is it true that $\gcd(ac,ab) = a\gcd(c,b)$?

Prove that $(0)$ is a radical ideal in $\mathbb{Z}/n\mathbb{Z}$ iff $n$ is square free

Why $\mathbb{R}[X]/(X^2+1)\cong\mathbb{C}$?

Study of rings of the form $R+I$

New posts in ring-theory

Groups of units of $\mathbb{Z}\left[\frac{1+\sqrt{-3}}{2}\right]$

What does $R-\mathrm{Mod}$ tell us about $R$?

Prime ideals in $C[0,1]$

If $A$ is generated as a $B$-algebra by $x_i$ and relations $r_j$, then $\Omega_{A/B}$ is generated over $A$ by $dx_i$ subject to $dr_j$.

Ideal products and calculating with ideals

Proof of the single factor theorem over an arbitrary commutative ring

Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal

Error in proof: $\mathbb{C} \cong \mathbb{C} \times \mathbb{C}$??

Prove that the set $a+b\sqrt{2}$ where a and b are rational without zero is a group under multiplication [duplicate]

Understanding the ideal $IJ$ in $R$ [duplicate]

$\mathbb Z [X] / (X)$ isomorphic to $\mathbb Z[X] / (X+1)$ isomorphic to $\mathbb Z [X] / (X+2015)$

Associative ring with identity, inverses, divisors of zero and Artinianity

An example of a Ring with many zero divisors

Inverse of a complex number (in Hamilton's pair representation)

Endomorphisms of modules satisfying chain conditions and counterexamples.

$R$ is an algebra over an infinite field. If $\exists$ ideals s.t. $J\subseteq \bigcup_{k=1}^nI_k$ then $J\subseteq I_k$ for some $k$

In an Integral Domain is it true that $\gcd(ac,ab) = a\gcd(c,b)$?

Prove that $(0)$ is a radical ideal in $\mathbb{Z}/n\mathbb{Z}$ iff $n$ is square free

Why $\mathbb{R}[X]/(X^2+1)\cong\mathbb{C}$?

Study of rings of the form $R+I$