When (a squared = a ) What is called this element?

In commucative unit ring why every prime ideal generated by idem potent element is maximal ideal ?

In Artin ring why every prime ideal is maximal ideal ??

I define the notion of "Galois class of L functions" in the following way: $A$ is a Galois class of L functions if and only if the follwing three conditions hold simultaneously: …

For two $n \times n$ nonnegative definite Hermitian matrices $A$ and $B$ over the real number field $\mathbb R$: Question1:Is there always a nonsingular matrix $P$ over the s …

"In this section, we deal with positive linear maps $\phi : A \rightarrow M$ between two unital C∗-algebra $A$ and $M$ with units denoted by $I$. In fact, we may assume that $A$ is …

Math people: The title is the question: What fields can be used for an inner product space? This question has been discussed in Math Stack Exchange with no definitive resolution. …

Let $I$ and $J$ be two ideals in $A$. Show that $\operatorname{Tor}_{1} (A/I, A/J) =\frac {I \cap J} { IJ} $ and $Tor_{2} (A/I, A/J) =\ker(I \otimes_ {A}J \to IJ )$. The first …

It is known that the set of ultrafilters on, say, the natural numbers $\mathbb{N}$, can naturally be endowed with the structure of a compact topological left semigroup (which fails …

Let $K$ bea field and $[n]={1,\ldots,n}$ and $K[x]=K[x_1,\ldots,x_n]$. For $\sigma={i_1,\ldots,i_k}\subseteq [n]$, denote $x_\sigma=x_{i_1}\cdots x_{i_k}=\prod_{i\in\sigma}x_i\in K …

Are there any definitions of quivers for algebras which are not basic or unital? I am reading the book Elements of the representation theory of associative algebras: volume one. Th …

From http://math.stackexchange.com/questions/346680/operating-on-a-set-of-sequences-such-as-adding-sequences-and-so-on-possible-ev Suppose that there is a way to code some set of …

For any monoid $M$, we can naturally construct a semiring $S$ as follows: Let the additive monoid of $S$ be the free commutative monoid on $M$ Let the multiplicative monoid of $S …

In 2005, prof. Emil Skoldberg developed a theory, similar to Forman's Discrete Morse Theory, but suited for arbitrary based chain complexes, in his Morse Theory from an algebraic v …

I'm writing an article on Lychrel numbers and some people pointed out that this is completely useless. My idea is to amend my article with some theories that seemed useless when t …