Mathematics
Profile Activity
Meta user
Network profile
128,703
reputation
13
127
309

rschwieb

PhD in Ring and module theory

If you also enjoy ring theory, you might enjoy the Database of Ring Theory.

I also have a blog now. For now I'm just offering advice for people aiming to start a math or math education career path.

If you want, you can buy me a coffee to show support for any of my work online.

Other interests: Clifford algebra/Geometric algebra, Applications of abstract algebra, geometry, Python programming and algorithm design.

Notes for myself:

Let $m$ and $n$ be integers in the ring of integers. Show that $m\mathbb Z$ contains $n\mathbb Z$ if and only if $m$ divides $n$

Prove $R\times S$ is not an integral domain

Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field

Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.

Is the ideal $I = \{f\mid f (0) = 0\}$ in the ring $C [0, 1]$ of all continuous real valued functions on $[0, 1]$ a maximal ideal?

If a ring element is right-invertible, but not left-invertible, then it has infinitely many right-inverses.

Prove that $A+I$ is invertible if $A$ is nilpotent

All group homomorphism from $ \mathbb{Z} _m $ to $\mathbb{Z}_n $

Right and left inverse

Order of general- and special linear groups over finite fields.

If $AB = I$ then $BA = I$

A linear operator commuting with all such operators is a scalar multiple of the identity.

In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.

What are the left and right ideals of matrix ring? How about the two sided ideals?

A ring element with a left inverse but no right inverse?

Explaining the product of two ideals

What's the motivation of the definition of primary ideals?

A ring $R$ which can be written as a direct sum of two ideals.

Ideal contained in a finite union of prime ideals

Proving $a+a =0$ for Boolean ring

$R^n \cong R^m$ iff $n=m$

Structure of ideals in the product of two rings

3,831
answers
38
questions
~3.9m
people reached

Communities (36)

Top Meta Posts
7
39

Top network posts

Top tags (450)

Score 4,962
Posts 1,973
Posts % 51
Score 3,656
Posts 1,592
Score 1,256
Posts 498
Score 1,154
Posts 553
Score 927
Posts 365
Score 772
Posts 369
View all tags →

Top posts (3,869)

All Questions Answers
Votes Newest
127 Is zero a prime number? Oct 29 '13
86 Are there mathematical concepts that exist in dimension $4$, but not in dimension $3$? Sep 4 '19
68 Stopping the “Will I need this for the test” question Jan 8 '14
52 Can there be an onto homomorphism from a ring without unity to a ring with unity? Feb 19 '18
51 Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian. Nov 15 '12
48 Intuitive definitions of the Orbit and the Stabilizer Dec 7 '12
46 Why don't Venn diagrams count as formal proofs? Feb 14 '13
45 What is the difference between a Hamel basis and a Schauder basis? Jan 7 '14
44 difference between dot product and inner product Aug 26 '13
44 “Negative” versus “Minus” Jun 11 '12
View all questions and answers →

Badges (449)

Gold

13

Rarest

Silver

127

Rarest

Bronze

309

Rarest

View all badges →