Related papers: Free skew Boolean intersection algebras and set pa…
The structure of quotient Boolean algebras in terms of cardinal invariants is investigated. Some results of Gitik and Shelah regarding atomless ideals are reproved and proofs are significantly simplified.
Given an algebra and a finite group acting on it via automorphisms, a natural object of study is the associated skew group algebra. In this article, we study the relationship between quasi-hereditary structures on the original algebra and…
Building on the work of K. Chiba (J. Algebra 263 (2003), 75-87), we present sufficient conditions for the completion of a division ring with respect to the metric defined by a discrete valuation function to contain a free field, i.e. the…
We show that free objects on sets do not exist in the category $bal$ of bounded archimedean $\ell$-algebras. On the other hand, we introduce the category of weighted sets and prove that free objects on weighted sets do exist in $bal$. We…
By quantizing the generalized Drinfeld-Sokolov reduction scheme for arbitrary $sl_2$ embeddings we show that a large set $\cal W$ of quantum W algebras can be viewed as (BRST) cohomologies of affine Lie algebras. The set $\cal W$ contains…
A class of associative (super) algebras is presented, which naturally generalize both the symmetric algebra $Sym(V)$ and the wedge algebra $\wedge (V)$, where $V$ is a vector-space. These algebras are in a bijection with those subsets of…
A. Tarski proved that the m-generated free algebra of $\mathrm{CA}_{\alpha}$, the class of cylindric algebras of dimension $\alpha$, contains exactly $2^m$ zero-dimensional atoms, when $m\ge 1$ is a finite cardinal and $\alpha$ is an…
The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set. Sambin's notion of an overlap algebra, although…
Let $S$ be a unital associative ring and $S[t;\sigma,\delta]$ be a skew polynomial ring, where $\sigma$ is an injective endomorphism of $S$ and $\delta$ a left $\sigma$-derivation. For each $f\in S[t;\sigma,\delta]$ of degree $m>1$ with a…
In this paper we present a simple approach to big Ramsey combinatorics of the Cantor set $2^\omega$. Using Infinite Dual Ramsey Theorem of Carlson and Simpson, we show that $2^\omega$, viewed as a topological space, has finite big Ramsey…
Let $R$ be an algebra over a commutative ring $k$. Suppose that $R$ is endowed with a descending filtration indexed on an ordered group $(G,<)$ such that the restriction to $k$ is positive. We show that the existence of free algebras on a…
We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A >>Cohen algebra<< is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of…
We show that the canonical involution on a nonabelian poly-orderable group G extends to the Hughes-free division ring of fractions D of the group algebra k[G] of G over a field k and that, with respect to this involution, D contains a pair…
Recent developments of Baxter algebras have lead to applications to combinatorics, number theory and mathematical physics. We relate Baxter algebras to Stirling numbers of the first kind and the second kind, partitions and multinomial…
We study scaling limits of skew plane partitions with periodic weights under several boundary conditions. We compute the correlation kernel of the limiting point process in the bulk and near turning points on the frozen boundary. The…
We construct a new bijection between the set of $n\times k$ $0$-$1$ matrices with no three $1$'s forming a $\Gamma$ configuration and the set of $(n,k)$-Callan sequences, a simple structure counted by poly-Bernoulli numbers. We give two…
For a set of nonnegative integers $S$ let $R_{S}(n)$ denote the number of unordered representations of the integer $n$ as the sum of two different terms from $S$. In this paper we focus on partitions of the natural numbers into two sets…
The set of all $\ell$-zero-sumfree subsets of $\mathbb{Z}/n\mathbb{Z}$ is a simplicial complex denoted by $\Delta_{n,\ell}$ We create an algorithm via defining a set of integer partitions we call $(n,\ell)$-congruent partitions in order to…
This paper develops a graphical calculus to determine the $n$-shifted Poisson structures on finitely generated semi-free commutative differential graded algebras. When applied to the Chevalley-Eilenberg algebra of an ordinary Lie algebra,…
Given a pair of smooth transversally intersecting manifolds in some ambient manifold, we construct an operator algebra generated by pseudodifferential operators and the (co)boundary operators associated with the submanifolds. We show that…