The tag has no wiki summary.

learn more… | top users | synonyms

4
votes
1answer
160 views

If questions are formalized as ideals of a boolean algebra, what kind of algebra of questions appears from Stone representation theorem?

Affirmative propositions make up a Boolean algebra, and Boolean algebras became part of classical algebra for over one century ago - in this sense they are "simple". But I did not encounter in ...
10
votes
0answers
179 views

Does every commutative variety of algebras have a cogenerator?

By a commutative variety $\mathcal{V}$ I mean a classical variety of algebras for some $(\Sigma,E)$, such that each pair of operations in $\Sigma$ commutes. Equivalently (i) every interpretation of ...
4
votes
0answers
82 views

How much do idempotent ultrafilters generate in terms of semigroups?

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 to be anything ...
3
votes
0answers
187 views

Adjunction algebra - is there anything similar to this in abstract algebra?

I call adjunction algebra a universal algebra with one binary operation denoted as the punctuation sign (;) "semicolon" (but I will be using only one space after it, not on both sides - to avoid going ...
3
votes
0answers
143 views

What can we say about a semigroup that's acted on by an ideal of polynomials?

This got no response on MSE, so posting here. Let $S = \{ (a,b) \in \Bbb{Z}^2 : \gcd(a,b) \neq 1 \} \cup (1,1)$. Then $S$ forms a semigroup. The operation being componentwise multiplication. Let ...
3
votes
0answers
105 views

Making an algebra the uniqe maximal one-sided ideal in another unital algebra

If $R$ is an algebra without a unit, then the standard unitisation $R^\sharp$ can have maximal one-sided ideals other than $R$. Thus, it is natural to ask about the following. Let $R$ be an algebra ...
2
votes
0answers
121 views

Rewrite sum of radicals equation as polynomial equation

My question is about a method described in Dr.Math forum for simplifying equations involving sums of radical functions. (The following is a transcription of the example given by Dr. Vogler): --- ...
2
votes
0answers
46 views

A category of partially-ordered commutative semirings; name/notation?

Organize $\mathbb{N} \cup \{-\infty\}$ as a semiring $S$ in the max-plus fashion. So in particular, we have $1_S = 0$ and $0_S = -\infty$. Then for every commutative semiring $R$, we get a degree ...
2
votes
0answers
107 views

Hall's paper on the profinite groups and Andre Weils “voisinage” notion

I am reading through a classical paper A Topology for Free Groups and Related Groups by Marshall Hall Jr. in which profinite groups are defined for the first time. There he defines on p. 129: ...
2
votes
0answers
133 views

Abelian Subgroup in an infinite non-abelian 3-group

Does an infinite non-abelian 3-group of exponent greater than or equal to 9 has an infinite abelian subgroup? I know that 2-groups and 3-group of exponent 3 has an infinite abelian subgroup. I wonder ...
2
votes
0answers
92 views

Lazard's $\Gamma_n(f)$ as cocycle

In Michel Lazard's "Commutative Formal Groups" Springer Lecture Notes, he defines an operator on a polynomial 3-cochain $f$ denoted $\Gamma_n(f)$, which defines as the $n^{th}$ homogeneous piece of ...
2
votes
0answers
98 views

classification of rank $2$ $\mathbb{Z}/p^n\mathbb{Z}$-algebra with invertible discriminant

Let $p$ be a prime number and $n$ be an integer. Let $A$ be an $\mathbb{Z}/p^n\mathbb{Z}$-algebra of rank $2$ whose discriminant is non invertible. In Serre's book lecture on the mordell Weil theorem ...
2
votes
0answers
105 views

Quivers for algebras which are not basic or unital.

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. The ordinary quivers ...
2
votes
0answers
120 views

Clifford algebra is graded separable

Let $D$ be an algebra of odd differential operators on a free module $V$, this algebra is isomorphic to the Clifford algebra $Cl(V^* \oplus V)$. Let $m$ denote multiplication map $$m : D\otimes D \to ...
2
votes
0answers
169 views

Idea behind choosing $\small f(x)$ as $c^{s}x^{p-1} \frac{[\theta(x)]^{p}}{(p-1)!}$ in the proof that $\pi$ is transcendental.

I am going through the article at this link, where the author proves that: "$\pi$ is $\text{transcendental}$ over $\mathbb{Q}$". Although, I understand the proof, I have some doubts. At page $6$, ...
1
vote
0answers
99 views

Definition of 'Koszul Ring' (in BGS)

In the paper 'Koszul Duality Patterns in Representation Theory' by Beilinson et. al, they give the definition of a Koszul Ring: A Koszul ring is a positively graded ring $A = \bigoplus_{j \geq 0} ...
1
vote
0answers
162 views

Is there any research of universal algebras axiomatized by non-Horn clauses?

A Horn clause in the language of a universal algebra is a disjunction of equations and of at most one inequality ("equation" and "inequality" are the terms used by A.Horn in his paper "On sencences ...
1
vote
0answers
241 views

Kunneth spectral sequence

In Rotman's Homological Algebra, 1st edition, there is written: Is every detail of 11.31-11.35 correct? Isn't the spectral sequence in 11.35 1st quadrant and not 3rd quadrant? Do 11.34-35 also ...
1
vote
0answers
83 views

Positivstellensatz for non-polynomial term

Can we use Positivstellensatz (P-satz) below for a non-polynomial term? P-satz: Let $R$ be real closed field. Let $f,g,h$ be finite families of polynomials in $R[X_{1} ,...,X_{n}]$. Denote by P the ...
1
vote
0answers
78 views

lattice coset counting

Let $m\geq 1$ be an integer and denote $B_m = \{-m, -m+1, \dots, m\}^n$. Suppose that $M\subseteq \mathbb{Z}^n$ is a module. By the structure theorem we can write $$ \mathbb{Z}^n/M \simeq ...
1
vote
0answers
131 views

Solving a system of rational functions

Given pairwise distinct numbers $c_1, c_2, \dots c_n \in \mathbb{C} \setminus \{0\}$, does the system of equations $$\frac{6}{c_k} + \sum_{i \ne k} \frac{2}{c_k - c_i} = \sum_{i = 1}^n \frac{1}{c_k - ...
1
vote
0answers
111 views

Is a certain group related to a primitive L function isomorphic to $Gal(\overline{\mathbb{Q}}_{\ell}/\mathbb{Q}_{\ell})$ for some $\ell$?

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: 1) every element ...
1
vote
0answers
286 views

about union of conjugate proper subgroups in a math paper

My question is about the shaded area in this image. Does the symbol $L=\bigcup_{g \in G} T^{g}$ means that $L$ is a union of sets or $L=\langle T^{g}, g\in G \rangle$? If it means the first one, then ...
1
vote
0answers
161 views

Invariant Ideals in Split Hopf Algebroids

Given a split Hopf algebroid $(S,\Sigma)=(S,S\otimes B)$ over $K$, Ravenel leaves as an exercise the proof of the following: An ideal $J\subset S$ is invariant under the action of the group ...
0
votes
0answers
57 views

Multiplicativity of the Ideal Norm

I asked this question on StackExchange twice, and was never able to get an answer. This is not quite a research-level question, but it is sufficiently difficult and interesting from a pedagogical ...
0
votes
0answers
37 views

Supersets of P-finite sequences and rings

P-finite sequences are a superset of C-finite sequences. While doing programming work, the question came up what generalizations or supersets of P-finite sequences have people described. In other ...
0
votes
0answers
42 views

Decomposition results for locally commutative semigroups

Every finite abelian group is the direct product of its cyclic groups of prime order, and every commutative monoid divides a product of its cyclic submonoids. Could these results generalized to ...
0
votes
0answers
64 views

Graded Betti Numbers of a Graded Ideal with Linear Quotients

Exercise 8.8 in Monomial Ideals by Herzog and Hibi: Let $I\subset S=K[x_{1},...,x_{n}]$ be a graded ideal which has linear quotients with respect to a homogeneous system of generators ...
0
votes
0answers
38 views

Graded Betti Numbers of a Stable Monomial Ideal

Exercise 8.8 in Monomial Ideals by Herzog and Hibi: Let $I\subset S=K[x_{1},...,x_{n}]$ be a stable monomial ideal with $G(I)=\{u_{1},...,u_{m}\}$ and such that for $i<j$, either ...
0
votes
0answers
42 views

About Linear Quotients of Square of an Ideal with Linear Quotients

Let $I$ be a monomial ideal generated by quadratic monomials $u_{1},...,u_{s}$ and suppose that $I$ has linear quotients with respect to this given ordering. Is it true or false that $I^{2}$ has ...
0
votes
0answers
177 views

Monomial ideals: isomorphism problem for commutative algebras?

Theorem 5.27 in Polytopes, Rings, and K-Theory (Bruns, Gubeladze - 2009 - Springer SMM) claims: Let $K$ be a field and $I\!\unlhd\!K[x]= K[x_1,\ldots,x_n]$ and ...
0
votes
0answers
69 views

Example of a ring whose minimals are annihilators of idempotents?

I'm looking for examples† of rings with the property that for each $P={\rm Ann}_R(a)\in{\rm Min}(R)$ then $a\in R$ is idempotent (ie $a^2=a$) † other than domains!
0
votes
0answers
103 views

Operating on a set of sequences - such as adding sequences and so on possible even when sequence is coded as number?

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 sequences into ...
0
votes
0answers
114 views

Structure groups and a special class of L-functions

Hello, Let $X$ and $Y$ be two mathematical objects such that there exists a canonical embedding $f:X\hookrightarrow Y$. I define the structure group of $Y$ relatively to $X$, denoted $Str(Y/X)$, as ...
0
votes
0answers
119 views

On X-s-permutable subgroups of a finite group

I want to prove Lemma 2.1(1) in the paper On X-s-Permutable Subgroups of a Finite Group by Min Bang SU, Yang Ming LI. It is on the web. This is my proof. . Since $H$ is $X−s−$permutable in $G$, then ...